Participant Testimonials

The Community in support of

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS)


Contents

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Persi Diaconis, Professor, Department of Statistics and Mathematics, Stanford University

I have participated in five or six meetings at Banff and am about to come up (mid-July) for another. First of all, I almost always say ``ßyes" to an invitation to Banff--it's spectacular, very well run, and productive.

I co-ran a meeting on a small combinatorial subject (De Bruijn sequences and Gray codes) a few years back that was amazingly productive: A journal's worth of surveys, solutions, and open problems is about to come out of it. The meeting was on a non-standard topic and it meant a lot to our participants to have a chance to get together. I have featured the interactions at the meeting in a chapter of my forthcoming book with Ron Graham (From Magic to Mathematics and Back). I think this meeting marked the emergence of this new subject as a field!

I have gone to all the major math conference sites over a twenty-five-year period. The Banff site is unique and, I think, my preferred site. Thank you for doing all you can for keeping this crucial treasure healthy and thriving.

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Robert V. Kohn, Professor, Department of Mathematics, Deputy Director, Courant Institute of Mathematical Sciences. New York University

I was a participant in the workshop on ``Facets of Heteroepitaxy" (Feb 2008). It was an excellent meeting - a timely topic, a well-chosen group of participants, good talks and even better informal discussions. This event was quite literally half physics and half mathematics; I was pleased to see that BIRS offered no resistance to such interdisciplinary activity - in fact it effectively encouraged it. The remoteness of BIRS made sure that people came for the whole week rather a few days - a feature many other centers lack, which did a lot to establish a sense of community among the workshop participants.

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William H. Sandholm, Department of Economics University of Wisconsin

I am writing to describe my experiences at a workshop held at the Banff International Research Station. The workshop was outstanding on all counts, thanks in no small part to the unique environment that BIRS provides. I attended the BIRS Workshop on Evolutionary Game Dynamics in the summer of 2006. Evolutionary game theory is a field that includes researchers from a variety of different disciplines. Economists (like myself), mathematicians, biologists, and physicists are among those with interests in this topic. Typically, conferences that include evolutionary game theory are held under the auspices of just one of these broader disciplines, with the consequence that it is easy to miss out on progress made outside of one’s own discipline. A few very large game theory conferences offer exceptions to this rule, but I have found that in these environments, one seldom has more than a brief conversation with people that one does not already know. The BIRS workshop I attended was unique in bringing together researchers from different disciplines, with each of the disciplines mentioned above being represented in roughly equal measure. The workshop involved about 40 participants and lasted about a week, which gave everyone the opportunity to speak at length with everyone else. Most importantly, the BIRS facilities were perfect for promoting interactions with new people. The conference center, lodging, lounges, and dining facility were all in close proximity to one another, providing countless opportunities to start up conversations about research with people one knew only by name, or not at all. The location at Banff also provided many opportunities for hiking and other outdoor recreation, and I can't think of a better way to develop a new idea than to take a long walk in a beautiful setting with a like-minded colleague.

Many of the people I met at the BIRS workshop I may well not have met otherwise. These introductions have lead to many seminar invitations that cut across disciplines (both to me by others and from me to others), and these in turn have introduced me to and stemmed collaborations with new networks of researchers. Let me mention just one example. During my presentation at the workshop, I briefly mentioned open source software I wrote for drawing phase diagrams for evolutionary game dynamics. Within a year, diagrams made with this software started appearing in physics journals. I had never even met a physicist working in game theory before I attended the workshop! To sum up, the BIRS workshop was one of the two or three most rewarding professional meetings I have ever attended, and from the point of view of crossdisciplinary interaction, it is the clear number one. I certainly hope that the Station will receive the funding it needs to continue to pursue its mission.

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Mark L. Green, Director Emeritus, Institute for Pure and Applied Mathematics, Professor, Department of Mathematics, University of California

As someone who spent 10 years running an institute-the Institute for Pure and Applied Mathematics at UCLA-and who is familiar with the Canadian mathematical scene through my time on the MRS committee, I want to say that I have always been impressed by BIRS. The points I would like to make are:

-The organizational side is handled admirably. As a workshop organizer, I have been able to concentrate on the science and know that the administrative side will be handled professionally. -It is a truly international resource that draws top-notch researchers on a regular basis. -The venue is conducive to research interactions and is especially favorable to junior researchers who do not yet know many of the senior people. Because everyone is on-site for the duration of the workshop, and participants eat all of their meals together, it is easy to get to know new people and launch new collaborations. -The quality of the workshops I have been to has been first-rate. -There is an open call for workshop proposals. BIRS manages over time to involve the math and other scientific communities very broadly.

This is a truly outstanding resource for Canada and for the world.

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Robert E. Megginson, Arthur F. Thurnau Professor, Department of Mathematics, Associate Dean for Undergraduate and Graduate Education, College of Literature, Science and the Arts, University of Michigan

A Native American myself, I have participated in two sets of workshops at BIRS on First Nations Mathematics. As far as I know, these are the only opportunities that have ever existed for mathematicians, First Nations elders, and educators to sit down to talk together about the issues that affect participation of First Nations people in Canada in the mathematical enterprise of the nation. No similar effort has been made here in the United States, and I found the experience quite valuable in aiding my thinking and planning for activities that enhance the mathematical engagement of Native Americans in the United States. Because U.S. and Canadian aboriginal peoples work together across our borders so extensively, such work tends to positively impact participation of all our peoples in mathematics in both nations. I also have done some preliminary work with Bill Barton, immediate past Chair of the Department of Mathematics at the University of Auckland, on the mathematical engagement of Maori in New Zealand, that was much informed by the BIRS workshops. As the demographics of North America and the world change, it is going to be exceptionally important that all of our nations not discard any of our mathematical talent before it has a chance to develop fully, and the BIRS workshops were quite helpful and informative for my own efforts to try to contribute to that.

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Arturo Pianzola, Professor and Chair, Department of Mathematical & Statistical Sciences, University of Alberta

I want to acknowledge the tremendous benefits that BIRS has yielded for the Mathematical Sciences community here in Alberta. We think of BIRS as one of us, and perhaps we tend to forget the complications that come attached to supporting such an ambitious enterprise.

I have personally benefited immensely from BIRS. During the last year, I attended a workshop where I had the chance to interact with researchers that I usually do not have the opportunity to meet. As a consequence, I became familiar with their point of view on one of the problems that I was working on. This lead to a beautiful paper in Mathematische Zeitschrift that I am very proud of. After the workshop I spent some time with one of my former posdocs, M. Lau (Windsor), and we finished working out some details of our joint work with V. Kac (MIT). This long paper (54 pages) will appear in Advances in Mathematics.

I also had a chance to visit BIRS with my long time collaborator Philippe Gille (ENS, Paris) as part of the Resarch-in-teams program. It was an intense but extremely rewarding week. BIRS provides the ideal environment for this type of collaboration. Two papers (to be submitted to elite venues) will thank BIRS for their hospitality.

I travel extensively to Europe, the U.S. and South America. I can attest that BIRS is a household name within the mathematical community, where it is viewed as an enviable place to hold a workshop or conduct research. We are very fortunate indeed to have BIRS in Alberta. That BIRS exists at all has a lot to do with your efforts, and on the behalf of all the members of the Department, we would like to offer our sincere gratitude.

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Charmaine Dean, Statistics, SFU

Bringing together the best researchers in the world to BIRS to discuss and challenge current thought in specific areas of science is an amazing experience. Not only are they stimulated by the problems, which are right up their alley of captivated and focused interest, but also by the setting where participating in the vibrant dialogue and exposition with other rich minds brings very rapid feedback and analysis of the constructs being considered. The engagement is at a very high level and provides an intimidating yet superb adventure for young researchers who are invited to these events; and what is most interesting is when one of these young researchers shines to the forefront and matches creativity and ideas with senior colleagues in attendance.

BIRS also provides a fabulous setting for melding interdisciplinary teams. Our national forestry team met at BIRS in our infancy, when we were just emerging as a network in Canada with top researchers in all the relevant fields for solving some specific problems in fire management and forest ecology. Working together at BIRS for a week secured our commitment to the project as we began to understand each other's language, semantics, areas of expertise and became immersed in the combined passion for research which grew from our interdisciplinary studies. This project has now significantly advanced forest fire modeling for fire suppression planning activities and out understanding of tree growth and mortality, fire-insect interactions and resistance to disease. We now have several countries interested in linking with out network and in utilizing our results. I am attaching a newsletter article which describes in nontechnical language some of our earlier achievements; excerpts from it may be helpful for the purpose of the testimonial.

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Robert M. Gray, Alcatel/Lucent Professor of Communications and Networking, School of Engineering, Stanford University

I have been involved with BIRS in a variety of ways. I have twice served as co-organizer of a workshop and I have served on the Advisory Board in the reviewing and selection of workshop proposals. The two workshops I helped organized were very different in their nature. One was purely technical, bringing together a broad range of scholars from the purely theoretical to the applied to discuss the interrelations of mathematical modeling with multimedia signal processing. The participants where extraordinarily diverse in their backgrounds and interests, yet found common ground at the borderline of theory, algorithms, and applications to speech, audio, image, and video processing for communication and analysis. The group was not one usually encountered at professional meetings, and the experience of discussing research with such a variety of individuals in such a beautiful setting was memorable. The ability to enjoy the Canadian Rockies with long hikes while discussing and thinking about new and old problems is unique to BIRS.

The second workshop involved bringing together people involved with mathematical, engineering, and medical research, but with the specific aim of sharing and developing effective techniques for improving the diversity in these fields by mentoring for diverse faculty, especially with regards to women. The participants ranged from undergraduate students considering academic careers to Deans of Engineering and a college president. The topics ranged from mentoring students, peers, and administrators to issues of balancing professional and family life. The workshop resulted in a paperback book detailing the presentations and discussions and all of the talks were made available on the Internet. The workshop had a profound effect on the immediate participants, who learned invaluable skills and established connections they still maintain. The book and Web presence spread the impact over a wider audience.

Both of these workshops were intense and productive and brought together diverse groups of people. All of the participants I have seen since then have reminisced fondly about the experience.

I have seen several workshops announced (or been invited to others) that I would very much have liked to attend, but other commitments interfered. This is evidence that the BIRS system continues to produce great ideas for focused research workshops.

During my two years of participation on the Advisory Board, I have been impressed by the dedication, enthusiasm, and hard work of the Board to judge fairly the many proposals and to balance all of the criteria in order to choose the best possible schedule. They have also worked hard to encourage resubmissions by potential organizers with good ideas, but whose proposals did not meet the high threshold. There is a great effort to encourage new directions while avoiding technical fads, and to balance well established areas with lesser known topics with significant activity or high potential.

BIRS has certainly had a major impact on both my technical research and on my avocation of supporting diversity in engineering faculty, it has initiated and enhanced many personal connections that would probably not have occurred without it, and it has provided a memorable experience in the process. I wish you every success in renewing your support, BIRS is an incredible resource for the theoretical and applied mathematics community, including my own electrical engineering community.

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Thomas Wong, MD MPH FRCPC Director, Community Acquired Infections Division Centre of Communicable Diseases and Infection Control Public Health Agency of Canada

As the Director of the Community Acquired Infections Division (CAID) of the Public Health Agency of Canada (PHAC) and one of the organizers of the 2007 “PHAC-MITACS Joint Symposium on Modeling Sexually Transmitted and Blood-Borne Infections” held at the Banff International Research Station (BIRS), it is my great pleasure to support your proposal to the sponsoring agencies of this unique facility.

From our first groundbreaking BIRS experience to this day, my public health team at PHAC continues to work with Dr. Jianhong Wu and members of the “Transmission Dynamics and Spatial Spread of Infectious Diseases: Modeling Prediction and Control” project team to whom we were first introduced in Banff. When I reflect upon why the enthusiasm for this collaboration remains, I am convinced that the magnificent environment itself provided myriad additional opportunities to exchange ideas and develop a deeper understanding of modeling sexually transmitted and blood-borne infections (STBBIs) than I have seen develop as intensely at many other workshops. Bringing together public health and mathematical professionals of such seemingly diverse areas of interest and experience – with little prior knowledge of one another’s expertise - worked and worked brilliantly.

Our 2007 experience at BIRS provided uninterrupted time and space for exchanging ideas; whether it was at the workshops, on breaks, or while sharing meals. I doubt that other venues would have inspired as much enthusiastic conversation and creative ideas as I overheard at BIRS, nor would they have produced as many collaborative initiatives as Jianhong’s team and mine have accomplished since Banff.

Over the past two years, MITACS and PHAC colleagues have continued to work together to identify and address public health knowledge gaps in modeling STBBIs. We have jointly hosted three successful workshops and organized a week-long academic course entitled “2009 MITACS Winter School on Mathematical Modeling of Infectious Disease” at the University of Ottawa for public health practitioners, PHAC staff, and students. Through relationships forged in 2007, we continue to work together in other ways as well: a presentation at the International Society for Sexually Transmitted Diseases Research (ISSTDR) in London, Englandthis year; modeling work on Chlamydia trachomatis; participation in several diverse ad hoc webcast training sessions; plus several collaborative articles on modeling of infectious diseases are pending, as is an ambitious CIHR proposal to address HPV. Our next joint venture will be international as we head to China to participate in the “Canada-China Colloquium on Modeling Infectious Diseases” next month.

BIRS is a valuable resource in the service of the world’s diverse scientific communities and a unique place where conversation and research ideas flow freely under respectful and optimal conditions. I am positive that your sponsoring agencies will agree with me when I conclude with certainty that our exciting work on mathematical modeling as a tool to address issues of concern in infectious diseases would not have begun nor continued without the new partnerships developed and strengthened by the lasting impact of our first shared MITACS/PHAC experience in the idyllic and inspirational setting provided by the BIRS. On behalf of my team at the Public Health Agency of Canada, I thank you again for having provided us this opportunity and wish you every success in continuing your excellent and influential work.

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Mark Lewis, Canada Research Chair in Mathematical Biology, University of Alberta

This email is to state that by consistently funding excellent research themes, BIRS has had an exceptional impact on mathematics and mathematical biology at the University of Alberta. I have personally participated in number of 5-day meetings, and the quality of mathematics and innovation has been outstanding. I expect to write two new research papers arising from collaborations at the meeting held at BIRS this summer (organized by Hillen and Perthame). There is an additional spin off: BIRS brings in top researchers from around the world and some of these stay and give talks/visit at U Alberta. In addition to co-organizing/participating in 5-day I have found that the weekend meetings/research in teams has proved invaluable for education (eg., hosting the PIMS International Graduate Training Centre in Math Biology Annual Research Summit) and collaborative research (eg., editing a book on bioeconomical models for biological invasions).

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Jean Dolbeault , UMR 7534 CNRS, Université de Paris-Dauphine

Je suis venu à de nombreuses reprises au BIRS, comme participant à des workshops (deux fois), comme participant à un « focused research group » (une fois) ou comme organisateur de workshops (deux fois). À titre personnel, j'ai donc amplement bénéficié des facilités offertes par le BIRS ; pour cette meme raison, il m’est aussi difficile de faire un bilan exhaustif des bénéfices que j'en en ai retiré dans mon travail de recherche. En simplifiant de manière sans doute excessive, on peut dire qu’ils sont de deux ordres :

Tout d’abord, c’est lors de certains de ces séjours que sont nées des idées qui ont débouchées sur des articles que je considère comme importants dans ma carrière scientifiques. Il est toujours délicat de retracer la naissance d’une idée, mais il me semble que la combinaison d’exposés pléniers, de discussions nées au cours de l’exposé ou lors des questions à l’issue de celui-ci, poursuivies en petits groupes ou en tête-â-tête avec d’autres participants, a constitué la formule fructueuse qui a débouché sur des résultats nouveaux. à cet égard, le BIRS me paraĒt un endroit particulièrement intéressant et approprié pour l’initiation et la gestation de contributions scientifiques réellement innovantes.

Ensuite, ces workshops m’ont apporté à chaque visite une vision stratégique de la recherche sur une question précise ; le fait d’avoir un projet scientifique détaillé, clairement identifié, qui détermine la liste des invités, me paraĒt crucial pour les thématiques émergeantes ou interdisciplinaires, qui m’intéressent plus que des domaines de recherche balisés, établis, voire « académiques ». Pour l'instant, le BIRS a su s’ouvrir à ces questions, en prenant parfois des risques, mais c’est aussi ce qui fait tout son intérźt si on doit le comparer à des institutions plus établies, comme le MFO à Oberwolfach. Pour dire les choses brutalement, les workshops auxquels j’ai assisté ont su échapper à une certaine sclérose que je ressens parfois au MFO, que ce soit au niveau des thŹmes ou de la liste des participants.

Dans un tout autre ordre d’idées, le BIRS me paraĒt un acteur important de la recherche mathématique au niveau international. Du fait des financements publics, nationaux ou européens, la recherche en mathématiques appliquées s’est largement développée en Europe au cours des vingt derniŹres années ; cela peut se mesurer par l’intensification des échanges, le nombre de doctorants et post-doctorants co-encadrés, l’augmentation de rencontres spécialisées, la création de nouveaux groupes ou d’institutions, ou, plus simplement par l’augmentation du nombre de travaux cosignés entre membres de plusieurs équipes. Cette évolution (tout au moins dans mon domaine de recherche : « équations aux dérivées partielles et applications ») me semble trŹs centrée sur l’Europe. Des liens se sont, bien entendu, développés avec des scientifiques d’autres pays (en particulier en Amérique Latine, en ce qui me concerne), mais plutôt à un niveau individuel. En Amérique du Nord, il me semble que les scientifiques qui ont accompagné ce développement européen l’ont fait de maniŹre trŹs isolée, souvent parce qu’ils avaient eux-mźmes des attaches personnelles en Europe. Le BIRS est un lieu qui fait exception à cette impression d’ensemble et me semble remarquable pour les interactions auxquelles il a donné lieu entre universitaires américains et européens. Dans chacun des workshops auxquels il m’a été donné d’assister, j' ai noté une proportion importante de chercheurs européens (pour lesquels il s’agit d’un déplacement important) qui ont toujours fortement interagi avec leurs collŹgues américains ; je n’ai pas été le dernier à bénéficier de ces interactions.

J'espŹre que ces impressions subjectives, que je n'ai pas cherchées à étayer par des données statistiques ou des exemples trop anecdotiques, contribueront à susciter un intérźt renouvelé pour le BIRS. Il s’agit d’une entreprise magnifique, originale, digne d’źtre poursuivie et développée, et qui, dans mon domaine d’activité, se situe au tout meilleur niveau international.

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John Friedlander, Professor, Department of Computer and Mathematical Sciences, University of Toronto at Scarborough

I have had the opportunity to attend a number of workshops at BIRS on number theory and also one on cryptography. I have enjoyed each of them very much and have benefited from the uniformly high level of talks and the exchange of interesting ideas in the conversations surrounding these. I am hoping to return again next spring, this time for the workshop on Diophantine Approximation and Analytic Number Theory being held in honour of Cam Stewart. A very special highlight of my experience with BIRS took place in August of 2007 when my co-author Henryk Iwaniec and I spent a week holding a (two person) ``Research in Teams" visit to work on our research monograph on sieve methods. We are just now completing this after close to five years of hard, though oft interrupted, effort and we were at a very important stage at the time of our visit to BIRS. We have high hopes that the book will prove useful to a wide audience, ranging from students with no previous knowledge of the subject right up to leading experts in the field. As a result, the book is necessarily rather long, in some places complicated and, especially for the students, it could prove somewhat difficult to navigate. It was quite important to us to tie things together with a preface which would help map out clearly what was going on and, at the same time, do so with sufficient ``poetry" so as to entice people to look more deeply into the mathematics.

At the time of our visit to Banff a large percentage of the mathematics had been done but the book was more a collection of topics rather than a coherent whole. The preface we wrote that week in Banff (with the concomitant alterations in the text) changed this dramatically. The excellent hospitality of the BIRS staff, the beauty of the surroundings there, and the freedom from external interruptions were crucial to this (and indeed, it was anticipation of that which had caused us to postpone writing, or even thinking about it, to this occasion). Although we have since added further sections to the book (indeed, one on ternary quadratic forms, was begun and almost completed during the same RIT visit), the preface has been only slightly altered in content, and not at all in spirit, from what we wrote that week. Things went so well that we are considering an application for a further RIT next summer timed to coincide with the last minute decisions on the final published form of our work.

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Richard Melrose, Professor, Department of Mathematics, Massachusetts Institute of Technology

I have found the Banff International Research Station to be excellently run and to have a stimulating atmosphere.

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Octav Cornea, Professor, Department of Mathematics, University of Montreal

It is a pleasure to acknowledge the important role the Banff Research Station has played in my own activities in the last few years.

I should first mention that, as a member of the Banff board for a few years, I was able to observe the high standards applied in the selection of the scientific workshops, and, as co-organizer of one workshop, I discovered the remarkable support and flexibility which allows organizers to focus on the scientific aspects of the events. Not to mention of course the great facilities situated in a truly unique environment.

However, I want to insist here on the direct impact that one Banff conference has had on my activity. This concerns a meeting in December 2005 on Symplectic Topology. It is at this meeting that I started a collaboration with Paul Biran. I knew Paul for some time before but the format of this meeting at BIRS was such that for the first time we could start to talk rather leisurely about some issues concerning a ``pearly'' model for the Floer homology of monotone Lagrnagian submanifolds. We did not go far during the week of the meeting but we did advance enough so that in the few month that followed we realized that many highly interesting applications can be deduced from this pearly model once it is rigorously established. We proceeded in the years that followed to deal with the relevant technical issues and infer the applications we envisioned as well as many others. Many of these results have been written up since then (in: ``Lagrangian Quantum Homology'' arXiv:0808.3989 to appear in the Yashafest 2007 volume, CRM-AMS, 50pp; ``Rigidity and uniruling for Lagrangian submanifolds'' arXiv:0808.2440, to appear in Geometry and Topology, 104pp; ``Quantum Structures for Lagrangian Submanifolds'' arXiv:0708.4221, 195pp). We are currently exploring some exciting relations with number theory.

This is I am sure just one example among many others. It does however reinforce my conviction that BIRS is an extremely valuable research facility and that its impact on the advancement of high-level research in mathematics is extremely significant.

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D.A.S. Fraser, Professor, Department of Mathematics, Department of Statistics, University of Toronto

Thank you for the opportunity to speak in support of the Banff IRS. Meetings and conferences are of course an important support for research activities. But workshops such as BIRS and Oberwolfach are truly the lifeblood. I have been fortunate to attend 3 workshops at BIRS and before that 2 at Oberwolfach The workshop format provides the close contact with those with shared research interests in a cooperative noncompetitive environment; the time period of the order of a week allows creative ideas to emerge and evolve and develop often to the point of publication level. My earlier experiences at Oberwolfach were dazzling and lead to substantial new research, in particular to extending higher order methods from essentially exponential model to the fully general asymptotic context (Biometrika. 1990). And then to find that Canada could equal and surpass the opportunities of Oberwolfach with BIRS! Most special was the BIRS workshop on the interplay of Statistics and High Energy Physics involving joint research with the HEP physics community (3 publications), and leading to current research on the interplay between Bayesian and frequentist statistical inference The BIRS contribution has been invaluable and I fully support the now North American tradition of the BIRS research meetings.

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Bruce Reznick, Professor of Mathematics, University of Illinois

I have had the pleasure of attending one meeting at BIRS, and am looking forward to an upcoming week in February 2010. I found that the environment was extremely conducive to effective collaboration. Not only was there an opportunity to meet many old friends in the same area, but I initiated a continuing mathematical communication with several postdocs. In my own work, I was inspired to present some material I had worked on for several decades and this catalyzed my desire to write it up for publication. See http://front.math.ucdavis.edu/0707.2156. In particular, I call your attention to page 25, in which I write: "We use this construction in the following example, which was inspired by looking at the regular pattern of pine trees below the Sulphur Mountain tram, during a break in the October 2006 BIRS program on “Positive Polynomials and Optimization”. The example is "The Banff Gondola Polynomials". BIRS is one of the great centers in the world for mathematical conferences, and I add my voice to many others in urging its continued support.

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V.Uma, Department of Mathematics, I.I.T Madras, Chennai-600 036, India

Participating in the BIRS workshop on "Group Embeddings: Geometry and Representations" during Sept 16- Sept 21, 2007 was indeed very inspiring. This was a unique opportunity to meet the experts in the field, interact with them and attend excellent talks. Moreover, I also got an opportunity to present my recent work in the presence of many experts, which was a very encouraging experience and an honor. I must say that it contributed a great deal in my continuing to work in this area and also strengthened my motivation to answer some of the questions raised during my earlier work.

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Anne Nouri, Professor at the Aix-Marseille I University, France

I have attended a 5 days workshop at Banff from june 21 to june 26 th 2009, and would like to express that it has been very fruitful to me on the reasearch level. The workshop entitled 'Theory and applications of classical and quantum kinetic theory', which is one of my subjects of research. I knew two thirds of the invited people, as known specialists of the field, and got into knowing the other third, which has been very interesting to me. The fact of gathering such a variety of very good specialists in the field from all around the world is impressive. Moreover, there were a few doctorate students, that brought hints about their new subjects of research. I should also mention that the fantastic frame of Banff helped at working hard, without feeling tired.

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Sheila S. Hemami, Professor School of Electrical & Computer Engineering, Cornell University

I am writing to express my gratitude to BIRS for the outstanding technical workshops that I have attended - Mathematics and Multimedia, in summer 2005 and Mentoring for Engineering Academia in summer 2007 (for which I was also a co-organizer).

The facilities and workshop logistics promote information discussion and collaboration, and additionally the participation model (i.e., participants must only travel to Banff) ensures that the workshops are maximally inclusive, especially for those who traditionally cannot afford to attend 4-5 day workshops.

Personally, I have benefited tremendously from BIRS. A collaboration that began during the 2007 workshop led directly to a sabbatical invitation, which has allowed me to move into a new area of research.

Again, thank you very much for all that BIRS has provided.

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Bert Gerards, Centrum voor Wiskunde en Informatica, Amsterdam

My testimonial about BIRS workshop: "09w5103 Applications of Matroid Theory and Combinatorial Optimization to Information and Coding Theory"

Being a matroid theorist I expected I would mainly find myself trying to pick up questions in coding and information theory where things from matroid theory may help. However it turned out to be totally different: there was a lot for me to learn about matroid theory itself. Much research represented from the information theory and coding side addresses issues and answered questions about matroids. Particularly regarding the so-called "Ingleton condition". In the matroid community there has been lately a renewed interest in it, but we thought we were on or own here and that the topic was barely investigated and almost forgotten. Through the meeting we learned that the opposite was true. I learned a lot during this meeting."

I should add to this that the infrastructure provided by BIRS is excellent.

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Colin McDiarmid, Department of Statistics, Oxford

I have visited BIRS twice, in 2003 and in 2007. The first was for a full workshop, the second with just 3 colleagues. Both times I found very valuable, stimulating and enjoyable. From the first I learned new material and made good new contacts (in particular concerning graphs on surfaces, about which I knew little at that point) that have been very helpful in some work since then. The second led directly to a paper that should appear soon. I am very much looking forward to visiting BIRS again soon, from 31 January to 8 February 2010, as the co-organiser of a workshop. The setting in BIRS encourages interactions, which are vital to stimulating research.

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Hans Weinberger, Professor of Mathematics, Emeritus University of Minnesota

I would like to fortify your case for renewal of BIRS by talking about its influence on my work. I was a participant of the mathematical ecology conference in the spring of 2008. The discussion which occurred during and after my presentation at this workshop has greatly influenced my work. It has recently culminated in a joint paper, which B. Li and I have just submitted to the Journal of Mathematical Biology.

In addition, my discussions with X, Zhao t at his workshop have led to a joint paper, which will appear in the journal Mathematical Biology and Engineering.

The BIRS provides an invaluable service to the mathematics community by creating opportunities for interactions with mathematicians with similar interests. It is a wise and fruitful investment.

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Jon-lark Kim, Assistant Professor, Math Dept, University of Louisville

I have participated for the 5-day workshop on invariants of incidence matrices organized by P. Sin, et. al.

The following is my experience: By visiting the workshop mentioned above, I could meet people including V. Tonchev, L. Storme, and other famous people, which would not be possible if there was no such workshop. I enjoyed the lecture given by Prof. Brouwer. As a coding theorist, I would like to investigate the codes generated by the incidence matrices of some geometric objects. His talk was helpful.

On the other hand, motivated by this workshop, I plan to organize a 5-day workshop at the Banff International Research Station (BIRS) in 2011 on coding theory and its related topics.

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Andrew Baker (University of Glasgow, Scotland) and Prof Dr Birgit Richter (University of Hamburg, Germany)

In addition to our report we, the organizers of the workshop ``New Topological Contexts for Galois Theory and Algebraic Geometry" would like to mention the following:

- BIRS provided a very productive working environment, as evidenced by the fact that several papers originated directly from the workshop:

Ausoni, Christian; Dundas, Bjorn Ian; Rognes, John: Divisibility of the Dirac magnetic monopole as a two-vector bundle over the three-sphere. Doc. Math. 13 (2008), 795-801

Vigleik Angeltveit, Michael Hill and Tyler Lawson, The spectra ko and ku are not Thom spectra: an approach using THH, G & T monographs volume 16, 'New topological contexts for Galois theory and algebraic geometry (BIRS 2008)'

- several papers appeared in the proceedings volume of the Banff workshop ( G & T monographs volume 16, 'New topological contexts for Galois theory and algebraic geometry (BIRS 2008)', http://msp.warwick.ac.uk/gtm/2009/16/) and were especially written for that:

Paul Goerss, Realizing Families of Landweber Exact Homology Theories

Kathryn Hess, Homotopic Hopf-Galois extensions: foundations and examples

Rick Jardine, The K-theory presheaf of spectra

Tyler Lawson, An overview of abelian varieties in homotopy theory

Peter May, What precisely are $E_\infty$ ring spaces and $E_\infty$ ring spectra?

Peter May, The construction of $E_\infty$ ring spaces from bipermutative categories

Peter May, What are $E_\infty$ ring spaces good for?

Susan Montgomery, Hopf Galois theory: a survey

Christian Schlichtkrull, The cyclotomic trace for symmetric ring spectra

- There were also a number of extremely useful survey talks at the workshop that helped to bring the communities of algebraists and topologists together.

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Robert Wilson, Professor, School of Mathematical Sciences at Queen Mary, University of London

The conference/workshop on permutation groups, 20-24th July 2009, was certainly the best conference I've been to in a long time. The combination of people brought together from all over the world made for an exceptionally lively conference. Every single talk was interesting and well-presented, which is a rare achievement indeed.

It stimulated my current research on new ways of looking at exceptional groups of Lie type, in various ways. Firstly, several participants told me about their own efforts in this direction. Secondly, some of the top people in the area appeared to be impressed by the simplifications I've achieved in some cases, which has encouraged me to continue this work further. Already since the conference I have a new construction of the compact real form of the $E_6$ Lie algebra, as a direct result of conversations during the conference. More work on $E_7$ and $E_8$ will probably follow.

Many thanks for a wonderful conference!

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Jonathan Kujawa, Dept. of Mathematics, University of Oklahoma

I have had the good fortune to participate in two BIRS workshops in the past several years. Although in different areas of representation theory, both were well organized, professionally run, and remarkably stimulating events. In addition to participating in formal and informal conversations about areas of current research, it provided the opportunity to collaborate with several individuals. I can readily identify several papers of mine which directly profited from my involvement in BIRS activities.

I look forward to future visits to BIRS and encourage the various funding agencies to continue their support for this valued component of the international research community in mathematics.

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Frantisek Matus Institute of Information Th. and Automation Academy of Sciences of the Czech Republic Prague

I participated recently at the workshop ``Applications of Matroid Theory and Combinatorial Optimization to Information and Coding Theory", August 7, 2009, and think that it was a great event for all the participants. I rate it personally as one of the very few scientifically best events I have participated at during the last five years.

The participants were combined from different communities: pure combinatorists, coding theory specialists, theoretical cryptographers, network coding and Shannon information theory engineers, quantum theory mathematicians, etc. A representant of each community presented a clear tutorial introduction to the topic and links to fields of common interest. The most valuable in my opinion were subsequent discussions that created a uniquely fertilizing atmosphere that helped, at least to me, to get a quick and effective orientation in several interacting fields of mathematics and information sciences. I gained several strong fresh ideas to elaborate upon for longer time.

The last but not least is the fact that I succeeded to meet for the first time personally some people whose scientific work I have known for more that 15 years. Even in the internet age personal communication has no electronic substitute.

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Prof.Kalman Gyory, Inst. of Mathematics, University of Debrecen, Hungary

Last year I was invited to give a lecture at the "Algebraic Geometry, Diophantine Approximation andArakelov Theory" workshop which was held in the Fields Institute, Toronto, between 20 and 24 October, 2008. My participation was very useful for me. I gave a 60 minutes lecture entitled "S-unit equations in number fields: effective results, generalizations, applications, abc conjecture". Several people were interested in my presented results.I hade the opportunity to discuss various mathematical questions and problems with other participants. During the workshop we continued our collaboration with Prof.Everste who also attended the workshop, and we made a good progress in writing a joint book of ours on the subject of the conference. The organization and hospitality during the conference was excellent, I am very grateful to the BIRS for the support.

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David Borthwick, Emory University

I attended the BIRS workshop on Mathematical Theory of Resonances, Sunday, October 19 to Friday, October 24, 2008, and I'm happy to comment on my experiences.

The BIRS setting is ideal for this type of focused conference. The facitilies provide ample space for discussion and interaction among participants. Since participants live and eat together, in addition to attending lectures, the forging of valuable new professional contacts is very much encouraged and in fact almost inevitable.

Here are two specific projects that benefited directly from my stay at BIRS: 1) After my lecture, P. Stefanov pointed out that some results of his from 2006 might be applicable in the context that I had talked about in the lecture. This suggestion has now grown into a 33 page paper that is nearing the submission stage. The paper was thus a direct result of my visit to BIRS.

2) During my stay, a collaboration with T. Christiansen, P. Hislop, and P. Perry developed on a project of common interest. At BIRS it was very easy for us to find joint discussion time and we were able to lay the groundwork for a joint paper. That paper is also currently in production.

My stay at BIRS thus proved to be a great inspiration to my research, and I am very grateful to have had the opportunity to attend the workshop.

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Dejan Slepcev, Carnegie-Mellon University

I participated in the workshop "Nonlinear diffusions: entropies, asymptotic behavior and applications" held from April 15 to April 20, 2006. Let me say that the workshop was of great interest to me and gave me the opportunity to hear about the current research of leading experts in the field. Moreover the relaxed atmosphere of Banff provided the opportunity to have a number of in-depth discussions with several researchers. Some of these have led to ongoing research projects. In particular the discussions at Banff I had with Jose Antonio Carrillo (ICREA and UA Barcelona) have started the research project that was latter joined by Stefano Lisini and Giuseppe Savaré and which resulted in the article "Nonlinear mobility continuity equations and generalized displacement convexity" which has been submitted to Journal of Functional Analysis. Also further discussions with Jose Antonio have led to the completion of the research project which resulted in the article "Example of a displacement convex functional of first order that will appear in Calc. Var. and PDE. (has been published online).

I wish you good luck with securing continued funding for BIRS,. I also look forward to further exciting workshops.

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Andrew Swann, Department of Mathematics and Computer Science, University of Southern Denmark, Odense M, Denmark

I took part in a workshop at BIRS early last year and found the whole experience excellent, meeting new colleagues particularly from Canada and the US, and renewing some older contacts. This was the first time I had been to Canada, and the new contacts established have been very helpful in several aspects of my mathematical life.

During in that week I essentially completed one paper I was working on, helped by the easy access to computing facilities; after publication one of the other participants, Christine TŅnnesen-Friedman subsequently used this as the starting point for a student project and her university. I also made good progress on two other projects, due to useful input from discussions at the meeting.

The talks were of a very high standard, with sufficient variation and breadth, that I learnt a lot in a short time. The chance to present my results to a relatively new and highly qualified audience was invaluable.

The centre deserves all the support it can get and makes a valuable contribution to international relations across mathematics.

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Professor Peter J. Olver, Head School of Mathematics, University of Minnesota

I would like to offer a couple of words in support of BIRS, based on several visits over the years.

Banff has rapidly evolved into one of the premier locations for holding intensive and innovative workshops in all areas of mathematics. It is playing an essential role in fostering the development of the North American mathematical research community and, by extension, the entire world.

The most recent workshop I attended, on Affine Convex Geometric Analysis, introduced me to a new research community that I was previously unaware of, but one that has many interesting connections with my current work in novel approaches to and new applications of the method of moving frames. I am continuing to develop contacts in this area, including visiting one of the organizers, Elizabeth Werner, to give a colloquium at her home institution this fall. Without the Banff workshop, this would have never happened.

I encourage all of my faculty here at the University of Minnesota, and other colleagues, to become involved in proposing and attending Banff workshops.

Banff is a unique venue for mathematics and mathematicians, and I completely and enthusiastically support its renewal.

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Art Owen, Stanford University

I attended on seminar at BIRS and found it immensely valuable. That seminar was number 08w5071, organized by Beran, Mizera, Johnstone and van de Geer.

For me it was good to get a snapshot of what people around the world are working on in statistics. This meeting collected together much of the best current work. It was very valuable to meet the other participants, some for the first time, others after long iterims. The setting at Banff is one of a kind, and very well suited to pondering big ideas, and having friendly yet deep discussions with other researchers.

One of the best insights I took away from the meeting was due to Rudy Beran. A speaker was explaining how prediction accuracy was, I paraphrase, the touchstone for comparing methods. Rudy pointed out that in the early days at least, Copernicus' predictions were less accurate than the Ptolemaic ones. I've since used that example in conversations with other researchers, particularly regarding the Netflix competition ... where Ptolemy seems to have won out.

I had a conversation with Debashis Paul, who later sent me a paper of his that proved useful in the forthcoming thesis of Patrick Perry, who has taken a postdoc in EE at Harvard University.

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Gary Greenfield, Editor, J. of Math and the Arts Professor of Math. And Comp. Sci, Department of Math & Comp. Sci, Univ. of Richmond

I was a participant at BIRS Workshop 07w5062 22-26 January 2007 "Innovations in mathematics education in the arts" which was led by George Hart. I am writing to let you know that not only did our group have a marvelous and inspiring time, but that the meeting led to some exciting, specific outcomes. I am the editor of the Journal of Mathematics and the Arts www.informaworld.com/JMA . Two of the participants at the workshop published reports as a consequence of the Workshop 1(3):203-207 and 1(4):263-265, and one of the participants, Mara Alagic, has just finished guest editing a Special Issue on this topic that will appear as Volume 3, Issue 3, September 2009 in which several participants are represented. Indeed the initiative will continue since in Volume 4 we will include a featured article on this topic in each issue. Further, the umbrella organization for mathematics and the arts, the Bridges Organization, held its annual conference in Banff for the second time in 2009 and BIRS provided the use of the Corbett Hall facility to selected persons in support of this venture. I was the recipient of BIRS support and I can assure you my associated editorial work would not have been possible without this advantage. I will be pleased to hear of your continued success at holding BIRS Workshops.

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Jeff Hirst, Professor of Mathematics, Department of Mathematical Sciences, Appalachian State University

am very happy to provide the following testimonial related to my participation in the BIRS workshop on Computability, Reverse Mathematics, and Combinatorics.

Overall, I found the workshop to be a fascinating and exhilarating experience. The content of the various talks and problem sessions was extremely interesting. The workshop has definitely had an impact on my research. Examples include:

(1) Carl Mummert and I have submitted a paper entitled "Reverse mathematics and uniformity in proofs without excluded middle." A pivotal insight leading to the completion of this project was provided at the workshop by Prof. Kohlenbach during one of the coffee breaks. (Please note: Carl was also a participant in the workshop.)

(2) Damir Dhzafarov, Tami Lakins, and I have started a project examining the reverse mathematics of polarized and stable versions of the Ramsey's theorem on trees. We hope to answer some of the questions raised about this topic at the workshop. One interesting facet of this work is that the definition of stability for partitions of trees seems to be less obvious than in the linear case. (Please note: Damir and Tami were not participants in the workshop, so the impact of the workshop extends to mathematicians who were not present.)

(3) Bernie Anderson and I are continuing our work on the reverse mathematics of infinite marriage problems. This project (reverse mathematics of a topic from infinite combinatorics) is related to the topic of the workshop, and we did discuss our work on this during the workshop. (Bernie was also a participant in the workshop.)

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Chengzhi Li Professor, Peking University, China

I am writing to you about my visit to BIRS for the International Workshop on Classical Problems on Planar Polynomial Vector Fields, November 23-28, 2008.

For me, it was an excellent experience. I have met many experts in my research field, learned many new developments from the talks, and discussed with some colleagues about our collaboration works. For example, during the workshop I discussed with J. Llibre from Spain about our joint works, now two papers have been submitted to journals.

On the other hand, your excellent services and the nice environment were strongly impressed on my memory. So I would like to thank all of you again.

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Craig S. Kaplan, University of Waterloo

I have had the good fortune of visiting BIRS on three occasions over the past four years. I attended the Renaissance Banff conference (05w5082) in the summer of 2005. Partly as a result of interaction with others at that conference, I was invited to attend a workshop on Innovations in Mathematics Education via the Arts (07w5062) in early 2007. In 2009 I returned for Renaissance Banff II (09w5134), this time as the conference chair. I am also currently helping to draft a proposal for a 2011 workshop.

Because most of my experience at BIRS is in the form of large conferences rather than small workshops, the outcomes are not the typical ones for BIRS. The focus of these events is not to work intensively towards publishable new results, but to present fresh interdisciplinary research, collected in a printed proceedings made available at the conference. In 2005 I presented two papers: ``TSP Art'', co-authored with Robert Bosch of Oberlin College, and ``Aliasing Artifacts and Accidental Algorithmic Art''. In particular, the paper on TSP Art has had a significant impact in the art-math world - artworks generated with the technique have appeared in art exhibitions, in books and magazines, and on the internet. Dr. Bosch has published further work on the subject, and he and I continue to discuss new ideas that will lead to publications down the road.

The most positive element of BIRS events for me is the distraction-free interaction made possible by the facility and its services. Within hours of the beginning of these events, a community of thinkers begins to coalesce. After a few days, ideas and inspiration are flowing so freely that it becomes impossible to keep up. I left Renaissance Banff II charged with new ideas and pursuing a couple of very specific collaborations that will likely lead to papers.

BIRS is one of a small collection of highly-valued mathematical retreat centres around the world. These facilities enable a level of focus and productivity that are simply impossible in day-to-day academic life. They must be protected and nurtured for the sake of basic research. But beyond that, BIRS is special. It happens to be nestled in one of the most beautiful places in the world. Moreover, the mathematical centre is surrounded on all sides by The Banff Centre, a world-renowned centre for the arts. The close proximity to the arts has been particularly beneficial to the interdisciplinary Bridges conferences - BIRS is uniquely positioned as a Bridges host. Finally, as a Canadian, I must say that it is a source of honour and pride to me that we can act as the home for this remarkable place.

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S. J. Dilworth, University of South carolina; E. Odell, University of texas at Austin; Th. Schlumprecht, Texas A&M, and A. Zsak, Cambridge University

We were the participants in a focused research group program in the Spring of 2006. Our original problem was studying partial unconditionality in Banach spaces. We achieved our goals in splendid fashion and much more. As a result of the intensive period of work permitted by our presence at BIRS, we were able to expand the problem to the more general setting of frames. Indeed a frame workshop at BIRS on Sigma-Delta Quantization during our FRG provided us with an opportunity to learn about frames and extend our results to these important objects in signal processing. Two papers ultimately resulted from our FRG.

`Coefficient quantization in Banach spaces' in Foundations of Computational Mathematics 8 (2008) no. 6 703-736

`Coefficient Quantization for Frames in Banach Spaces' (with Pete Casazza) in J. Math. Anal. Appl. 348 (2008) no. 1 66-86

BIRS is a most valuable institution for mathematical research and we vigorously support its continuation.

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Ogul Arslan, Ph.D. in Mathematics, University of Florida

was a participant of Invariants of Incidence Matrices workshop at BIRS during the first week of April 2009. BIRS hosted 40 mathematicians from all over the world doing research on similar topics in that workshop. I had a chance to meet the researches in person and discuss mathematics with them. The fact that all of us stayed and ate at the same place was one of the great things about BIRS. I had a chance to talk to almost every mathematician and exchange some mathematical ideas. One other nice thing about BIRS was the staff who worked there. They made everything so easy for us. I am in touch with some of the mathematicians that I met at the workshop and planning on working together with them in the near future. I gratefully thank all the sponsors of BIRS.

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Edson A. Coayla Teran, Universidade Federal da Bahia

I have had a nice professional experience when visit the BIRS, I worked with my mates in the project: Optimal Control of Stochastic Differential Equations with delay. Now we are working in a report. Furthermore I participated in some talks on the theory of Stochastic Differential Equations with delay.

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Professor P. E. Jupp, School of Mathematics and Statistics, University of St. Andrews, Scotland

I write to say how impressed I was by BIRS on my first visit in March 2009, when I attended workshop 09w5112 "Data Analysis using Computational Topology and Geometric Statistics". This was a splendid inter-disciplinary workshop, which opened my horizons to work done by people in fields parallel to my own, and has influenced the direction of my research. The opportunities to interact with other mathematicians are excellent. Natural comparisons for me to make of BIRS are with the other international mathematical centres that I have visited: Oberwolfach, the Newton Institute in Cambridge, and CIMAT in Guanajato (Mexico). It seems to me that BIRS is in the same league as these three. I wish it continued success.

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Thomas LEPOUTRE (UPMC and INRIA, Paris)

I have lucky enough to be invited at the workshop

Multiscale Analysis of Self-Organization in Biology

(12-17 July), and it has been a wonderful experiment. I have to deeply thank the institute to give me this opportunity to present my work (through a poster session) to people from all over the world. The conditions of organization were excellent, any question I asked received a quick answer, and this gave me opportunities to ask questions to very intersting persons. As a European guy, this was for me a great chance to be in contact to Canadian and more generally with North American mathematics. The approach is sometimes quite different and I definitely think that the best way to improve is to see what are the tools other people are using. As a simple PHD student I have to admit that I am not fast enough yet to produce a paper in such a short time, but discussions were definitely helpful (and supportive) for a specific subject I started to work on shortly before.

I was a pleasure to be there, I hope I will come back,

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Pierre Ille, Institut de Mathématiques de Luminy, France

During the last four years, I attended the meeting Infinite Graphs in October 2007 and I organized a focussed research group Indecomposable Binary Structures in June 2009. Both meetings gave the opportunity for interesting discussions with colleagues who do not share truly the same area of expertise, which allows us to envisage new points of view and new kinds of results. Of course, profitable discussions in the same framework are natural and numerous, and lead sometimes to solve problems or at least to make important advances. For instance, I solved with another participant a new conjecture on the minimal indecomposable extension of a binary structure during the focussed research group in June 2009.

The scientific and technical management of the BIRS is very efficient and permits the participants to feel comfortable. The nice location of the BIRS helps as well. Finally, I would like to insist on the fact that the BIRS provides different types of meetings and hence different and rich scientific experiences to its guests.

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John Holbrook, Professor of Mathematics Emeritus, University of Guelph

A couple of years ago I participated in a BIRS workshop on mathematical structures in quantum information theory. The workshop was first-class in every respect. It was very stimulating for my own work in that field and I met several colleagues with whom I have contiued to work. The workshop was a springboard for a number of subsequent developments. I think in particular of striking recent results in the theory of higher-rank numerical ranges. The workshop put a spotlight on crucial problems related to this concept and before long many of these had been solved.

BIRS is an extremely valuable international resource for mathematics, and it is especially important for Canadian mathematics. It deserves generous support from all levels of government and from the mathematical community.

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Peter Hinow, University of Minnesota

My participation in the BIRS Workshop 09w5070 "Multiscale Analysis of Self-Organization in Biology" (July 12-17) was a very pleasant and inspiring experience. It was a great opportunity to meet again with old friends and to meet for the first time with new people. The accomodation and the food left nothing to be desired.

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Denis Hirschfeldt, Professor of Mathematics, The University of Chicago

I attended the workshop "Computability, Reverse Mathematics and Combinatorics" held at BIRS in December 2008. This was a wonderful meeting that brought together nearly all the most important researchers in this area, and BIRS was an ideal location for it, providing an environment where, for five days, this group of researchers, which included computability theorists, proof theorists, model theorists, computer scientists, and combinatorists, could discuss the current state and future of the area in both formal and informal settings. The emphasis on open problems and future research directions was particularly welcome, and I think we will feel the impact of this workshop and the open problems list it generated for years to come.

I would like to mention one exciting development that has already emerged from the workshop. During one of the sessions devoted to discussing open problems, I presented one from a paper I co-authored with Richard Shore. Three of the other participants in the workshop, Chi Tat Chong, Steffen Lempp, and Yue Yang, learned about that problem from my presentation, and they have since solved it using a beautiful method that could prove very useful in future work on nonstandard models of arithmetic and their application to reverse mathematics. Indeed, their work also filled a gap in one of the central papers in the reverse mathematics of combinatorics (two of whose authors, Peter Cholak and Carl Jockusch, attended the workshop), and answered several questions in another recent paper (one of whose authors, Jeff Hirst, attended the workshop). Their paper, "On the role of the Collection Principle for $Sigma^0_2$-formulas in second-order reverse mathematics", will appear in the Proceedings of the AMS.

I very much enjoyed my time at BIRS, and learned a great deal from the workshop. I think that BIRS is a key resource for the mathematical community.

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Vic Patrangenaru, Associate Professor, Department of Statistics, Florida State University, Tallahassee

The meeting Data Analysis using Computational Topology and Geometric Statistics in March under the auspices of BIRS, was the best out of many workshops I attended : extremely well organized, informative, with top participants in the exciting emerging fields of statistics on manifolds and computational geometry and topology. The five days workshop with a half day break in the middle was an excellent idea. The meeting facilitated communication between researchers of diverse backgrounds between brilliant researchers and creators of this important field at the core of modern statistics and mathematics. The BIRS organizers did a superb job with lodging, allowing us to freely meet in the lounge and giving us access to their smartly organized library and internet access. That meeting triggered for me new collaborative work, and inspirational material for two chapters of a monograph of Nonparametric Statistics on Manifolds, I am currently working on, that I expect will help Multivariate Analysis growing into a more attractive area of Data Analysis. The organization and the surrounding views were surpassing our expectation, and the altitude could only help our minds and souls being more creative than usual.

All in all, it was a very rewarding experience for me, and I beleive for all the participants in our meeting. Thanks organizers! Thanks BIRS! Thank you for giving us the opportunity to share our wonderful memories about this workshop.

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Raymond Yeung, City University of Hong Kong

I just attended the workshop

09w5103 Applications of Matroid Theory and Combinatorial Optimization to Information and Coding Theory

I find the workshop most interesting, to the extent that I would rate it as one of the best workshops I have been to. It provides a unique environment for people with different but related fields to get together to discuss problems. It looks to me that something substantial will be derived from this workshop subsequently.

Thank you BIRS for offering this opportunity.

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Ivan Arzhantsev, Associate Professor, Department of Higher Algebra, Faculty of Mechanics and Mathematics, Moscow State Lomonosov University, Russia

I have participated in the workshop "Group Embeddings: Geometry and Representations", September 16-21, 2007, Banff International Research Station. I enjoyed this event very much: high-level mathematics, well-prepared talks on actual research projects, perfect organization, nice environment and working facilities. It was a nice opportunity to present our joint results with my German colleague Prof.Dr.Juergen Hausen on Cox rings and Geometric Invariant Theory at this workshop having representatives of many leading research groups as the audience. We gave two talks successively, and during next days there were several interesting and rich in content discussions.

In my opinion, existence of BIRS is very important for further development of mathematical sciences and fruitful collaboration between researchers all over the world.

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Eric Woolgar, Mathematics, University of Alberta

I co-organized a 5-day workshop at BIRS in 2008. It was the easiest meeting I ever organized. Because of the infra-structure that was already in place at BIRS and the Banff Centre, I didn't need to spend any time on the usual logistical issues such as arranging accommodations, meeting rooms, and food, and I didn't have to worry about raising funds to cover speakers' local expenses because BIRS provides local accommodation and meals during the workshop.

I could therefore concentrate entirely on the scientific programme.

We were able to attract some of the top people in the field of geometric flows. This field is really exploding in countries like the US, Germany, Australia, and China, but currently there is not some much expertise in Canada, so it was quite important to bring these international experts here. Since then, there have been three other meetings on this subject, all held in Europe. Canadians, including some of us from the University of Alberta, have been invited speakers at these meetings, and I'm certain that would not have been the case if not for the exposure that came out of our BIRS workshop.

Participants from our 2008 BIRS workshop have asked me to organize another, so I will be submitting a proposal for 2011. The enthusiasm has been such that I already have more prospective participants than BIRS can accommodate. I therefore very much hope that BIRS continues to be fully funded in the years to come.

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Volker Runde, Mathematics, University of Alberta

I just learned from my chair, Arturo Pianzola, that BIRS has to renew its funding now.

Let me just say that I wouldn't know really what to do if BIRS were not to have its funding renewed. Having a world class institution like BIRS literally at our doorsteps is a major factor contributing to the excellent research environment at the U of A.

I have co-organized two workshops there and have participated at about three or four more, and I can testify that BIRS provides a uniquely stimulating environment for mathematical scientists from around the world that is rivaled by very few places elsewhere (only Oberwolfach or Luminy can possibly compete). BIRS puts Alberta on the world map as far as mathematical research is concerned. For mathematical researchers around the globe, Alberta is best know as the province within whose borders BIRS is located (and whose government has had the vision to fund it).

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Richard Craster, Centennial Professor, Mathematics, University of Alberta

I have attended one BIRS workshop in the past (05w5028 Viscoplastic fluids) and am looking forward to the one that I am co-organising next year (10w5035 Small scale hydrodynamics). The BIRS workshops are, rightly, world famous among the mathematics community and have a very strong reputation for bringing together scientists in a wonderful environment condusive to research. In my case, the 05w5028 workshop allowed me to renew my collaboration with Neil Balmforth (this led to several publications in J Fluid Mechanics, QJMAM, Proc R Soc Lond A, J Non-Newt Fluid Mech) and rekindled my interest in that subject. The workshop itself was attended by a diverse mi of engineers and scientists and notably there have been follow-up meetings elsewhere in the world. I really valued the opportunity to attend and, as I say, I am looking forward tremendously to the meeting in February. I wholeheartedly support the BIRS program and wish it continued success.

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Lorens Imhof, Hausdorff Center for Mathematics, Associate Professor of Statistics, Bonn University

I took part in a BIRS workshop in 2006. The workshop was very well orga- nized with an attractive selection of participants from various backgrounds. I would like to mention the following points. • At the time of the workshop, I was relatively new to the řeld and the workshop gave me a good overview of topics of current interest. At least řve talks had a direct impact on my own research. • I got (and stay) in contact with an economist that I probably would not have met otherwise. • During the workshop a colleague and I made substantial progress on a joint pro ject. The resulting paper has appeared this year. The BIRS workshop was one of the most fruitful scientiřc events I have attended.

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Michael Strevens, Philosophy Department, New York University

I attended a BIRS workshop on probabilistic models of cognitive development (09w5100). The workshop gave me the opportunity to (a) meet a number of important researchers in this broad area, (b) talk to researchers I already know but otherwise seldom see, and (c) develop and explain some of my own recent work on cognitive mechanisms for learning probabilistic properties of observed mechanisms. It was an extremely fruitful five days for me; I continue correspondence with, and in two cases plan on future collaborations with, some of the people I talked to at the workshop.

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Alina Bucur, IAS and UCSD

have been to Banff only once, for the WIN-Women in Numbers conference in November 2008 organized by Kristin Lauter (Microsoft Research), Rachel Pries (Colorado State University) and Renate Scheidler (University of Calgary). The aim of the conference was to bring together women number theorists at various stages of their careers (from graduate students to senior mathematicians) together and encourage them to network and start collaborating with each other. In my case, they were successful on both counts beyond expectations. To begin with, it was a really nice atmosphere to be surrounded by so many women in my area. Usually one meets one or two women at a conference, but here there were 40 or so of us. It made me feel less isolated in a world still so dominated by men. It made it easier to get to know the other participants and learn about their research and their experience in general. In fact, everyone had such a positive experience as far as networking was concerned that we decided to start a Women in Numbers Network (WINN) and invite other women number theorists to join us. The group has now a wiki page and is planning follow-up activities, including a conference proceedings volume that will be published be the Fields Institute. Together with two other people I met at Banff I am organizing a special session at the Joint Meetings in San Francisco in January 2010. Ours is just one of the sessions organized by members of WINN. Also, we are planning to have more WIN conferences, In fact, three of the participants to the original conference are applying to BIRS to organize the second conference of what we hope will be a series. We plan to organize such conferences every 2-3 years in various parts of US and Canada. And maybe one day on other continents.

But most importantly, I have started to work on a project outside my previous area of expertise with three other participants at the WIN conference in Banff, Brooke Feigon (University of Toronto), Chantal David (Concordia University) and Matilde Lalin (University of Alberta, Edmonton). The situation was similar for all of us, the project was close but not quite in any of our fields. I personally learned a lot of new math working on it, especially algebraic geometry, that I would have not delved into otherwise. We already have a preprint submitted for publication that came out of this collaboration, concerning statistics for the trace of Frobenius on p-fold covers of the projective line over finite fields. It can be found at

http://arxiv.org/abs/0907.5434

We also have another related project in mind, concerning statistics of zeros of the zeta functions for the same type of curves. This new project will be joint work with another woman number theorist, Kaneenika Sinha from University of Alberta.

In addition to being exposed to new math, the fact that I did some work in a new area of number theory made me talk to a whole new set of people that I had no contact with before.

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Burglind Juhl-Joricke, IHES, France

The conference at Banff which I attended addressed several important directions of complex analysis and geometry. I met some colleagues whom I knew before only by name.

I may report even about a very concrete detail: from a talk by Sukhov I knew about his joint paper with Tumanov about the existence of certain pseudoholomorphic cross-sections - a result which I knew would be the basis for generalizing a new construction of pseudoconvex envelopes to domains in arbitrary complex manifolds (instead of Stein manifolds).

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Anatoli Ivanov, Penn State University, Wilkes-Barr

It was indeed a great pleasure to organize a workshop and attend the BIRS itself in June 2009.

During my 25 plus years of research activities I have been to many research centers and facilities around the world, and I can testify that your Centre is definitely one of the best and on the very top in all regards. It provides an excellent accommodation and other support, and the place is just gorgeous in the middle of Canadian Rockies.

Research-wise, the one week stay certainly has had a very positive and strong impact on my own research. I needed to spent a lot of time to prepare myself for the running of the workshop. Before the workshop I have put quite a strong effort to review most recent results and accomplishments in the field, which has brought me to a new level of understanding of certain things and to a number of good open problems to approach. As a result of the preparation, and the preparedness during the one-week workshop itself, I was able, in collaboration with others, to quickly advance with the soluiton in a couple of spesific problems that will result soon in submitted for publication papers. But most important outcome, from my prospective, is that I have a whole new research direction of stochastic functional differential equations, which makes a large and imporatnt part of my current research agenda.

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Elisabeth Werner, Case Western Reserve, Cleveland

In March 2006 I participated at the 5 day workshop “Convex and Discrete Geometry” at BIRS. For me, this was a very instructive workshop as it provided me with more in depth insight into the current research in discrete geometry.

In January 2009, I was given the opportunity to organize a 5 day workshop “Affine Convex Geometric Analysis” at BIRS together with M. Ludwig and A. Stancu. Overall: This was a wonderful experience. Before and during the event, the competent and friendly staff at BIRS helped organizing everything so that the workshop ran smoothly. The workshop itself was a success. It managed to bring participants of different areas to BIRS, researchers working in convexity, differential geometry and computer science- not only for this event. Indeed, it was the starting point for closer ties between a group of researchers working in a certain area of differential geometry and researchers in affine convex geometry that have been intensified and continued since. We got very positive feedback from all the participants, concerning the scientific aspects of the meeting, but also with respect to the perfect everyday organization due to the existing structures at the BIRS facility. In particular, there ware quite a number of graduate students and post docs participating and I know from my students that this event at BIRS has been extremely helpful for their mathematical development not only because of the new mathematics they were exposed to but also because of the opportunity to interact with a broader mathematical community.

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Fred Brauer, Mathematics, University of British Columbia

I have been involved in two summer schools at BIRS, in 2004 and 2009. In these schools we tried to collect a diverse group of students from a variety of disciplines and introduce them to mathematical epidemiology. The long range goal was to increase the awareness of non - modellers to the usefulness of mathematical modelling and to increase the pool of modellers. We have run schools in other locations in 2006 and 2009, but the environment at BIRS in which students were together much of the day and could concentrate on learning and organizers and instructors could think in depth about what could be done differently was invaluable. We believe that the development of these schools has been a useful contribution to epidemiology.

I was also involved in a workshop in 2008 which collected a diverse group of people covering mathematics, epidemiology, and public health and really exposed all participants to many perspectives. Again, I believe that the mixing of a diverse group of people was an essential ingredient. The BIRS environment encourages informal contacts and this contributes greatly. In my opinion, interdisciplinary groups are the ones that gain the most from BIRS workshops because they really mix the groups. Personally, I have learned much about how people who are concerned with communicable diseases in real life as opposed to the ivory tower of mathematical modelling think, and this has influenced my work considerably.

From an organizer's point of view, the fact that accomodations, meals, and work facilities are taken care of with very little need for organizers to be involved is a great help.

The establishment of BIRS was a great contribution by the scientific community to the development of science, and its continuation is essential for Canada to continue to be a player in the world of science.

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Seongtag Kim, Dept. of Mathematics Education, Inha University, Incheon, Korea

I visited BIRS for 5-days workshop “Geometric and Nonlinear Analysis” in Aug. 2006. This workshop was concentrated in my research fields. The mathematician and talks were so excellent which cannot be found in any other place. This workshop was very nice and provided an excellent chance to communicate ideas and develop new results. During the workshop, I got an idea to extend my results in a more general setting. I strongly support BIRS program.

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Richard A. Shore, Department of Mathematics, Cornell University

I did want to express my gratitude for the BIRS conference on Computability, Reverse Mathematics and Combinatorics in Decmeber 2008. It was a very successful conference with a lot of interchanges among people with different approaches. In addition to the talks we had a problem session whose results have been put together and are available on the site. One problem raised by someone from Japan was solves at the meeting by someone from the U.S. and there should be a paper coming out of that work. From my own perspective, a coauthor (Hirschfeldt) presented some problems arising form our work and three people (Chong and Yang from Singapore and Lempp from Madison) began working on it at the meeting. Their work has now produced a solution that I find very original in that it applies an analysis of nonstandard models to solve a problem that seems purely combinatorial. Their methods also solved problems of Cholak, Jockusch and Slaman and of Dzhafarov and Hirst. They have already written the paper. In the other direction, I became interested in a problem presented by Marcone (Italy). We have started a new collaboration and have good partial results and some hope for a full solution. I certainly had the impression that the other participants much enjoyed the conference and expect that there must be other collaborations that resulted in addition to the ones with which I have been involved.

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Toke Meier Carlsen, Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway

I have had the great fortune of being participating in several conferences at BIRS, and each time has, in addition to being an absolute pleasure, been very inspiring and useful for my research. BIRS seems to me to be very professionally organised, the setting is beautiful, and the conferences I have been attending at BIRS have managed to attract some very interesting people, and have thereby lead to some very interesting and productive scientifically discussions. This has for me lead to new collaborations and new insights.

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George A. Elliott, Canada Research Chair in Mathematics, University of Toronto

My opinion is that BIRS is one of the very best centres of its kind in the world, perhaps the best--although with Oberwolfach, with for instance its fully complete mathematical library, the competition is of course very stiff. (The Oberwolfach meeting centre gets national attention at the highest level--already from the days of Hitler, I guess!) One of its strong points--besides the setting!--is of course its accessibility--with Calgary receiving direct flights from all over the world. Also, BIRS is much closer to the airport than Oberwolfach is to any of the major airports surrounding it. Its embedding in the Banff Centre is a major coup. Aside from the efficiency in the common use of infrastructure, one is piggy-backing on a world-level cultural institution--and not to mention the musical and other cultural events (a number of times such events have actually been organized by BIRS, or by a particular workshop), the spin-off of very high-level accommodation, catering, and physical exercise facilites again is world-beating--after all, Oberwolfach does not not have an opera house! Concerning the scientific aspects of the workshops, would people travel from all over the world (at their own expense), and would organizers (including the board of directors!) act virtually as slaves to make the experience possible, if it were not crystal clear that such a meeting is an unmissable opportunity?! All of the meetings I have attended, in several somewhat different areas, by the way, have resulted in rewarding new acquaintance, and further collaboration with people that I already knew well. One striking example was the workshop on locally finite Lie algebras in 2003--not only was this closely related to my earlier work on approximately finite (AF) C*-algebras, but also, as a result of this conference I made progress towards formulating my classification techniques (including the so-called Elliott intertwining argument) in a more abstract setting (now completed in a paper about to appear in Advances in Mathematics), which in particular allowed me to make a conceptual contribution-- already during the meeting--to the problem (being considered already by a number of participants in the workshop) of classifying locally finite countable groups (a problem on the face of it apparently unrelated to C*-algebras--but, as it turned out, intimately related--with, in an important case-- inductive limits of sequences of finite products of simple alternating groups--in fact the same answer as for AF algebras!). In conclusion, I look forward to the meeting next year that I am involved in organizing, on the classification of C*-algebras, a sequel to the BIRS workshop on this subject a year and a half ago. I have the impression from participants of that meeting that this was one of the most successful meetings on this subject ever. (There have been at least twenty meetings at least half devoted to this subject, one of the most active in operator algebra theory.)

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Oleg Pikhurko, Carnegie-Mellon University, Pittsburg

I've been to BIRS four times. The workshops at Banff are always impeccably organized and have a good mix of participats: from most prominent researchers to aspiring graduate students.

The scientific level is also very high. For example, because of my participation in the workshop 07w5117 "Infinite Graphs", I got seriously interested in (hyper)graph limits and flag algebras. By now, I have written 2 papers where I use these tecniques: "An Analytic Approach to Stability" (submitted to Discrete Mathematics) and "The Minimum Size of 3-Graphs without a 4-Set Spanning No or Exactly Three Edges" (submitted to the European Journal of Combinatorics). The latter paper was presented at the most recent workshop 09w5035 "Probabilistic and Extremal Combinatorics" and the related informal discussions with many other participats were very stimulating and helpful.

The setting of the Banff Center is perfect for holding such regular meetings and I hope very much that the BIRS will continue its programs for many years to come.

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Bill Freeman, Computer Science, MIT

As a matter of fact, this workshop at BIRS may have been the best one I've ever attended. The participants were great, and the setting and facilities and great organization in the Banff Center made everything easy and comfortable. I'd love to organize or participate in another workshop at the Banff Center!

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Derek W Hoiem, Department of Computer Science, University of Illinois at Urbana Champaign

The workshop was very productive, and I had a great time. Thanks so much for your management!

The duration and seclusion of the workshop made it uniquely well-suited for extended discussion. I emerged with a stronger sense of the direction of the field and a greater awareness of the extent and potential of the Internet's impact on computer vision, particularly by creating new applications and opportunities for massive-scale data collection and annotation.

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Rick Szeliski, Microsoft, Washington

I thought that this week's BIRS workshop was the best focused workshop I have ever attended in my 25 years of doing computer vision research and attending conferences and workshops in my field.

The level of interactive discussion was the greatest I have ever seen, and the workshop was a wonderful way to get up to speed on the latest advances in Internet computer vision and large-scale object recognition. The discussion we had on alternative approaches to recognition and on methods and objectives for collecting large data sets were invaluable, and I believe that they will significantly increase the rate of progress in our field.

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Komla Domelevo, Université de Toulouse, France

I had the chance to participate in the workshop "Reaction-diffusion and Free Boundary Problems" (number 06w5045, March 18-23, 2006).

This workshop was one of the most insteresting and stimulating one that I ever attended. It gave me the opportunity to discover new topics, such as the Freidlin-Wentzell theory relating the geometry of some diffusion systems to processes taking place on graphs thanks to appropriate asymptotics. It is a very interesting work to me since I'm interested in the extension of these results to some cases arising in the case of premixed flames. Other than that the conditions of work offered in the center gave me enough time to discuss with colleague and learn more about their research interests.

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Vijay Pande, Associate Professor of Chemistry and, by courtesy, of Structural Biology and of Computer Science

I am traveling right now, so my response will unfortunately be brief. However, I am very eager to support the BIRS grant renewal. I have had a wonderful experience there. Bringing together a broad group of researchers has lead to high impact conferences. Also, the setting of BIRS makes it particularly conducive, since people always enjoy traveling there. I am eager to go to future BIRS conferences and wholeheartedly support future funding to make this possible.

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Harjoat Bhamra, Sauder School of Business, University of British Columbia

The paper I presented at Banff was recently accepted at the Review of Financial Studies. Presenting it at Banff helped me get feedback from some of the leading academics in my field, which most likely increased the quality of the paper, making it easier to publish.

I also made contact with academics who have been able to give me advice about my current research, in particular the mathematical aspect of it.

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Amelia Crowfoot Clark, Old Sun Community College

I found my involvement with the BIRS workshop very engaging especially as it relates to the indigenous ways of knowing. Having elders meeting with mathematicians was an exciting opportunity to participate in the exchange of western and indigenous knowledge.

As a First Nations mathematics educator, I have found the relationship between western science and indigenous knowledge very intriguing. Having hosted a science camp for youth since 1992 at a First Nations College, Old Sun Community College, we have incorporated Siksika knowledge with western science and have had amazing experiences.

Thank you for allowing me to participate in the workshop I attended a couple of years ago.

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Phillip Geissler, Assistant Professor, Department of Chemistry, University of California, Berkely

The workshop I attended at BIRS last summer was uniquely stimulating and productive in several ways. On a subject that bridges applied mathematics and chemical physics, it drew an atypically broad audience, and created a remarkably successful forum for communicating across disciplinary boundaries. The environment and workshop schedule allowed for continuous discussions that I found to be exciting and fruitful. I think BIRS is ideally situated for hosting this kind of workshop and would be thrilled to attend another.

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Adam Oberman, Assistant Professor, Department of Mathematics, Simon Fraser University

BIRS is a fantastic institution - it's the one of the legs that mathematical research in Canada stands upon. Please do everything you can to keep this institution going.

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Navin Madhavprasad Singhi, Department of Mathematics, University of Mumbai

I am very happy to reply to you about my experience at BIRS. Workshop was great and all the staff was great. I enjoyed a lot those 5 days. BIRS experience indeed helps a lot in research activities of a researcher. I recall from my talks with other colleagues - when I told them that I am going to BIRS, they had a very positive reaction. Many of them had been to BIRS and were very happy with their experience. Indeed I was even thinking of organizing with some others some workshop in BIRS.

I hope these few words help you in your finding success. I recommend for full support and expansion. An expansion with larger activities will indeed be good for BIRS.

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Steven Krantz, Professor, Department of Mathematics, Washington University in St. Louis

I am very fond of Banff. It is a wonderful research environment, the surroundings are spectacular, the accommodations are great, and the food is very good indeed.

My first experience at Banff was with a group of four that worked together closely for about two weeks. We produced a nice paper--actually while we were there at Banff!!--and published it in a good journal.

My second experience at Banff was a conference on holomorphic mappings that I organized. It was attended by about 30 people and was dynamic and exciting. For myself, some of the talks led to a nice new paper which I am quite proud of. This was in collaboration with one of the other participants. I've also developed some new working relationships, and gotten some nice invitations, because of contacts made during the meeting.

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Atul Narang, Assistant Professor, College of Engineering- Chemical Engineering

In 2004, I spent 4 days at the BIRS workshop entitled ``Dynamics, Control and Computation in Biochemical Networks." I recall this workshop as the most productive meeting I have ever attended. The discussions with the other participants played a vital role in shaping the direction of my research in systems biology. Moreover, thanks to the workshop, I established a close collaboration with biologists at the University of Alberta.

I sincerely hope that the sponsors will continue to support the unique and truly outstanding program at BIRS.

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Avner Ash, Professor, Department of Mathematics, Boston College

I attended a conference at BIRS last summer on the Trace Formula. This conference enabled me to resume contact with many colleagues I hadn't seen for a long time, and I made valuable new contacts. Although I don't do research directly in the area of the conference, I found that the series of lectures and discussions helped fill me in on the recent amazing advances in the field, and stimulated my own research.

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Vincent J. Carey, Associate Professor, School of Medicine, Harvard University

I attended a BIRS session in statistical analysis of microarray data a few years ago. The arrangements were exceptional, the program was excellent, and a number of collaborations ensued. I strongly endorse the continuation of the program.

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Justin McCrary, Assistant Professor, School of Law, University of California, Berkely

I attended a workshop early in my career (prior to beginning my first job, at the University of Michigan, in Fall 2003) on the regression discontinuity design, a research design that approximates, under mild conditions, the gold standard of a randomized controlled trial. The introduction to this powerful research design was coupled with the introduction to many important scholars working in this area. Both of these introductions were important for my subsequent career.

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Kevin R. Vixie, Researcher, Mathematical Modeling and Analysis, Los Alamos National Lab

I attended a workshop in 2004 on image analysis that made a significant contribution to me being a serious part of the recent mathematical image analysis phenomena. While at the workshop, not only did I strengthen ties I had, but I made new acquaintances with people like Curt Vogel who subsequently worked with our team at Los Alamos.

I also moved closer to Bill Allard, spending a great deal of time with him during and after the conference at Banff, getting into the nitty gritty of technicalities involving geometric measure theory.

As a result of all this and a few other significant events like it (before and after) I was positioned well when I decided the time had come to move from Los Alamos to a university, and I was able to get an offer for my whole lead team from WSU.

How did Banff figure into this? Was it *the* key factor? No, but it was a very important one. The other factors - chairing the summer school at IPAM/UCLA, organizing a highly successful workshop on image analysis at LANL in 2002, writing papers because of my association with allard, esdoglu, etc - all these were important. But Banff figures prominently in my mind in creating and or strengthening ties I have with numerous individuals in this area - people like Tony Chan, Curt Vogel, Andrea Bertozzi, Stacie Levine, Stan Osher, Bill Allard, Selim Esedoglu, etc. etc.

And it is the ties that Banff and IPAM and IMA create that may be the most important thing they do - the most important thing they could do - in the service of the fields of science and mathematics that they touch.

In my opinion, Banff, IPAM, IMA, and the other institutes may very well be the best, most productive use of money that the funding agencies have at their disposal.

So, I support the institutes (all of them and the idea of getting even more of them) wholeheartedly and will say so to anybody who will listen.

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Florin Diacu, Professor, Department of Mathematics and Statistics, University of Victoria

Thank you for your message and for giving me the opportunity to thank BIRS again. Indeed, there is a lot to say. I participated in five workshops and one research-in-teams activity since BIRS was created. I was happy to organize one of the workshops. All these activities have been extremely beneficial to me and to the fields I am active in.

The event I organized with Don Saari brought together not only the best world experts in celestial mechanics but also young and promising students. With one of them I published two joint papers in the Transactions of the American Mathematical Society. The research-in-teams opportunity produced another paper in the same journal. This research would have never been done without the chance BIRS offered. Also, one of the workshops in creative writing in the mathematical sciences in which I participated led to the publication of the first anthology of fiction, non-fiction and poetry written by mathematicians, and I was glad to be one of the authors of this acclaimed volume.

To sum up, BIRS is THE BEST research institute of its kind in the world, and I hope that it will outlive me by at least a century.

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Joseph A. Wolf, Professor, Department of Mathematics, University of California, Berkely

The Banff International Research Station plays an important role in North American science. Its programs bring together Canadian, Mexican and U.S. researchers, and bring them into contact with European and Asian researchers, for scientific programs at the highest level. The only comparable facility in the world is the Mathematisches Forschungsinstitut Oberwolfach in Germany. The scientific impact of the BIRS program is very great. I took part in a program on locally finite Lie algebras, and I think that almost every participant learned aspects of current research in that field of which he had not been aware. This led to strong advances, combining the algebra and the analysis on the corresponding Lie groups and their homogeneous spaces, which have now become important areas in mathematics.

My personal experience at BIRS is in two parts. There was the locally finite Lie algebra program I just mentioned, where the research and discussions certainly took place under the very best conditions (with fruitful results). In my case it led to several papers and some collaborative research on parabolic subalgebras and principal series representations.

Second, there is the upcoming program in mathematical physics that Jedrzej Sniatycki and I are organizing to take place in summer of 2010. We expect this program to be important in evaluating the mathematical and the physical aspects of string theory vs. E8 theory, and so to continue the strong tradition of BIRS programs at key scientific crossroads.

In brief, BIRS plays an important role in current scientific research, and it is important that it continue to bring research scientists together under circumstances that foster discussions, collaborations and future scientific developments.

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Dmitry Khavinson, Professor, Department of Mathematics, University of South Florida

I have visited Banff twice in the last four years, for a workshop on Laplacian growth in July 2007 and for Research Group in July 2008.

My experiences have been superb.

The workshop allowed me to make important contacts with mathematical physicists that resulted in several joint papers and jointly submitted research proposals and several on-going projects in the general area of Hele-Shaw flows and Complex Analysis. One of the results of this workshop was a recent paper I published with two other participants M. Mineev-Weinstein and M. Putinar launching the generalization of Hele-Shaw flows, processes of general elliptic growth.

The research group experience allowed us to have intense discussions for a week on an old problem concerning distribution of zeros of complex polynomials. A survey that we are writing jointly reporting on our progress is in the works.

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Jill Pipher, Professor, Department of Mathematics, Brown University

I was one of four participants in a ``Research in Teams" a couple of years ago, along with M. Lacey, S. Petermichl, and B. Wick.

Our week at BIRS was incredibly productive and efficient. The accommodations and facilities were perfect for our research effort. Our focused activity coincided with a weeklong workshop in spectral theory/partial differential equations and we also had productive discussions with these participants.

This week at BIRS made it possible to complete our project, which was recently published in the American J. Math, as well as made possible future projects, one of which was recently published in the proceedings of the El Escorial Conference in Harmonic Analysis.

I was so impressed with the research environment at BIRS that, when the opportunity presented, I applied again for a Research in Teams effort with C. Kenig, S. Hofmann, and S. Mayboroda, which is scheduled for April 2010. I am delighted to have the opportunity to pursue our project at BIRS.

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Steven J. Miller, Assistant Professor, Department of Mathematics, Williams College

I have attended one conference at BIRS: L-functions, ranks of elliptic curves and random matrix theory workshop (7/12/07). This was an extremely valuable conference for me. The center fostered a terrific environment for collaboration. I have since begun working with new people on a variety of projects; this has led to my traveling to England twice and one of my colleagues visiting me here for a month. I am planning on organizing a workshop on the theory and applications of Benford's Law in the near future, and I (and several of my colleagues) am all strongly considering applying to have it at BIRS.

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Robert Krasny, Professor, Department of Mathematics, University of Michigan

I participated in the two-day workshop in October 2008 on ``Singular Phenomena in Nonlinear Optics, Hydrodynamics, and Plasma" organized by Pavel Lushnikov. This was my first visit to the BIRS in Banff. The workshop was interesting and valuable for me professionally, in particular as I formed some new contacts and renewed existing ones. I would certainly look forward to participating there again and will consider proposing to organize a workshop there in the future.

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Michael Hartley Freedman, Department of Mathematics, Princeton University

My time at BIRS was very enjoyable, and rewarding from a professional perspective. As well as providing a rare opportunity to present my work to an interested audience (I live geographically distant from most people working in my field), it was a great opportunity to make new contacts. One of these in particular led to a collaboration that culminated in a published journal paper. This paper would not have existed without the conference at BIRS.

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Joachim von zur Gathen, Professor, Department of Mathematics, University of Paderborn

I attended two BIRS workshops, the last one in 2006 on polynomials over finite fields. I presented ongoing work on some counting problems in finite fields, and during my presentation Hendrik Lenstra, another participant, found the perfect solution to a problem for which I only had a partial solution. The published version (Finite Fields and Their Applications 14(2008), 944-978) includes on page 977 the following acknowledgment: ``Hendrik Lenstra found his precise bound for Ragot's probability during my lecture at the 2006 Meeting on Polynomials over Finite Fields and Applications in Banff. I thank him for his permission to include this here, and BIRS for making the conference possible." In addition, two other participants, Cathy O'Neil and Antonia Bluher, contributed results and ideas that are vital for my current work.

These are just three examples of how the BIRS workshop has contributed to advances in research that without that chance of meeting people would probably not have happened.

I am a regular organizer of workshops at Oberwolfach, and appreciate the international atmosphere and interaction that I find there and at Banff.

My research has profited a lot from the BIRS workshops. I am pleased to see it is flourishing, and hope that it will continue in this way.

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Shmuel Weinberger, Professor, Department of Mathematics, University of Chicago

I am writing to express my gratitude for the wonderful atmosphere at BIRS. I have been there twice, once for a topology conference, and once as an organizer with Jim Davis for a meeting connecting geometric group theorists, operator algebraists, and topologists.

The staff was enormously helpful and the environment was just perfect. It was a fruitful meeting - I am aware of a number of developments on central problems that resulted from our meeting (two important ones are a paper of Fisher and Silberman on groups that don't act on any manifold, and one by Bestvina showing that mapping class groups have finite asymptotic dimension). I very much look forward to the next occasion that I can return.

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Peter Taylor, Professor, Department of Mathematics and Statistics, Queen's University

ß BIRS is an awesome place. Our professional lives offer us very few chances to be together with colleagues from all over the world for five discussion-oriented days. In June 2006 I attended the Evolutionary Game Dynamics Workshop. My interactions there led directly to an invitation to spend the Fall 2007 at Martin Nowak’s Program for Evolutionary Dynamics at Harvard and the problems we worked on there opened a completely new area of research for me and ultimately led to a recent PNAS publication. And now I am lucky enough to have won a workshop slot in 2010. This facility clearly deserves a sustained high level of support.

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John McKay, Researcher, Department of Mathematics, Concordia University

This is a wonderful research centre.

I have benefited from BIRS. As with this much research it is a question of opportunity. One can find enormous benefits unforeseen when deciding on applying to some meeting. It is not possible to forecast ultimate benefits - even of chance encounters.

I believe (and have much evidence of) there are inadequate communications between and even within departments. Places such as BIRS are helping to alleviate this problem.

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Cheryl Praeger, ARC Federation Fellow and Professor of Mathematics, University of Western Australia

My first visit to BIRS was in November 2008 for a small workshop on graph symmetry organised by Joy Morris. I had met Joy occasionally at conferences but did not know her well. The program was extremely well directed, with participant lecturers requested to lecture on specific topics.

I was asked to lecture on arc-transitive graphs, and the theory I had developed for analysing families of such graphs. The method involved proving closure under forming normal quotients, identification of ``basic" graphs in these families, and application of powerful group theoretic methods to analyse the basic graphs. This prompted me to refine my own understanding of this methodology, and both to reinterpret earlier analyses and to propose open research questions regarding various important families of graphs.

Following the workshop Joy asked me how this might apply to give new understanding of the class of strongly regular graphs. We began a research project - that has extended to include also Pable Spiga, another early career researcher whom I met for the first time at the workshop in Banff. We have been exploring this by frequent exchange of tex files, and have a first paper almost ready for submission. In addition, Pablo will make an extended visit to work at my university starting later this year.

I look forward to my next visit to Banff in July when I will be one of the organisers. I can only hope that workshop will approach the success of the one last November.

I want to say thank you to BIRS for the wonderful support and spectacular environment provided for mathematics. This is an extremely valuable service to the scientific community - to mathematics. I truly hope the granting bodies will see how well their investment has turned out and will offer continued funding.

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Simon Warfield, Director, Computational Radiology Laboratory (CRL), Children's Hospital Boston, Associate Professor, Department of Radiology, Harvard University

My experience at BIRS during for a medical image computing workshop was very positive. It was a tremendous opportunity to work closely with colleagues on the most pressing problems in medical imaging, and to discover recent progress made towards solving these problems.

The environment was extremely well suited to facilitating scientific interchange. The food, hospitality and setting all worked together to make connections between the investigators. The outcome was significant and long-lasting ties between experts in the field.

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Chitat Chong, Professor, Department of Mathematics, National University of Singapore

I wish to state that BIRS has played a significant role in promoting international collaboration and supporting scientific research. I was a participant at the Workshop on Computability and Reverse Mathematics in Banff in December 2008. It was my first visit to Banff and the experience has been most memorable.

The meeting provided me with an opportunity to interact with researchers I know and those I met for the first time. It was scientifically rewarding. Specifically, it was at the meeting that my colleague Prof Yue Yang and I became interested in the proof-theoretic strength of the combinatorial principle PART and discussed with Prof. Steffen Lempp of Wisconsin on possible ways of attacking this problem.

We made a quick start and worked on it in between talks and in the evenings while we were in Banff. Ideas germinated but we were not able to resolve the difficulties. Upon our return to respective institutions, we continued to discuss the problem over Internet. By early May we had the solution and the first draft of the paper was completed. I visited Wisconsin in late May where the final version of the paper was brought up for discussion. The paper has since been circulated and has attracted interests from several colleagues who pointed out refinements to the results we have proved and further applications. I would say that it was the BIRS meeting that started it all.

I believe that there were many instances where scientists have benefited in very tangible ways from participating at meetings organized in Banff. BIRS has contributed significantly to advancing science in service of the world scientific community.

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Richard Evan Schwartz, Professor, Department of Mathematics, Brown University

My experience at Banff: I enjoyed the workshop quite a bit. I found the talks to be very interesting and thought-provoking, and I learned some things that I didn't already know about. My 4 favorite topics at the conference were: 1. Ashwin's conjecture about periodic islands in piecewise isometric maps.

2. The dynamics of the 1-dimensional Schrodinger equation

3. Rauzy's example of a specially interesting interval exchange transformation

4. A great survey talk about the state of the art on aperiodic tilings.

The subject of low complexity dynamics has lots of amazing computer-inspired conjectures and not so many proofs. What I found exciting about the conference was the sheer number of interesting and unsolved problems. The conference has definitely inspired me to keep thinking about problems in this area.

One concrete way I benefitted from the conference is that Sergei Tabachnikov (another participant) and I started talking about a topic called the pentagram map. Sergei had actually been in Banff the previous week, with Valentin Ovsienko, to discuss this map. Sergei's conversations with Ovsienko and myself eventually led to a 3-way joint paper, in which we solved a conjecture I had made about the pentagram map almost 20 years ago - that it is a completely integrable system. This collaboration is still going strong, one year later.

I thought that the conference facilities were generally excellent. It almost goes without saying that the beautiful setting made the trip worthwhile independent of the mathematics. I loved walking around Banff and also hiking in the nearby mountains. My wife came with me, and I was able to find a nice balance between attending the conference and spending time with her. She enjoyed sketching and photographing the scenery around Banff, especially the plants and flowers.

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Ian Frigaard, Professor, Department of Mathematics, Department of Mechanical Engineering, University of British Columbia

In October 2005 I was fortunate to co-organise a workshop at BIRS on visco-plastic fluids. These fluids arise in a wide range of applications: industrial, geophysical, food production, medical, etc... and over the years many application scientists had developed their own niche's in using these fluid models, largely independently from one another. At the same time, the mathematical world had made some advances in theoretical and numerical methods for these fluids, but these were largely separated from the application scientists.

This meeting, in the wonderful setting of Banff, with the professional organisation of BIRS and hospitality at the Banff centre, was very well attended and a resounding success. The meeting of this core of key people in the field has led to collegiality and improved communication. There has been a resurgence of interest in viscoplastic fluids (with special sessions & minisymposia at the 2 major rheology meetings in Europe and North America, every year since). A special issue of Journal of non-Newtonian Fluid Mechanics was dedicated to papers presented at the workshop. The workshop also spawned a biennial series: ``Viscoplastic Fluids, from Theory to Application", which met in Monte Verita, Switzerland in 2007, will meet in Cyprus in November 2009 and has a 4th conference planned for Rio de Janeiro in 2011 - hopefully back to BIRS for 2013! In each of these meetings we have retained the collegiality, sought always to build bridges between people and include new areas - trends all started at BIRS.

It is important to note that the main impact of this workshop series is not on mathematics, but on a wider community of applied scientists. The 2007 meeting was focused at geophysical problems and the 2009 meeting at industrial applications. Having said this, the mathematical community is somewhat unique in the collaborative and communal organisation of research resources. There are few (if any?) disciplines that possess independently run scientific centres that are able to bring together people in this way, and also few countries that have similar treasures.

My own association with this series has certainly had a very positive impact on my career: becoming a frequent organiser of minisymposia and similar in this sub-field, increasingly called on for reviewing of papers and grants, invited lectures and a recent invitation to the editorial board of Journal of non-Newtonian Fluid Mechanics.

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David Tartakoff, Professor, Department of Mathematics, University of Illinois at Chicago

I had the privilege of attending, and speaking at, one of the weeklong workshops at BIRS a few years ago and must say it was an extraordinarily productive experience - inspirational even.

The blend of excellence of the participants, and their care, in a spectacular setting, permitted the most fruitful exchange of ideas and growth.

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Tucker Carrington, Professor, Department of Chemistry, Queen's University

The BIRS workshop I attended was great. It gave me a chance to meet Canadians working in my field.

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Ashish Goel, Associate Professor, Department of Science and Engineering, Stanford University

I took part in the conference CAAN in 2004 in Banff. It was an excellent experience. Along with meeting people in an informal setting, one of the main attractions for me was meeting several Canadian researchers that I normally don't interact with. One example is Martin Demaine, whose papers I have since read with interest. I would love to attend another event at BIRS.

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Justin Corvino, Assistant Professor, Department of Mathematics, Lafayette College

Thank you for your efforts at BIRS. It is truly a marvelous setting for scientific workshops. I had the pleasure of attending a December 2007 Workshop on Minimal Submanifoldsshops. I am pleased to see it is Ŗourishing, and hope that it will continue in this way.

Since I work at a small school (Lafayette College), I especially value opportunities such as the BIRS workshop to meet with both well-establish colleagues (such as Rick Schoen, Mario Micallef, Greg Galloway, Claudio Arezzo, Jingyi Chen, Ailana Fraser), and also to meet some of the younger people entering the field. In this world where we are very connected by technology, it remains important to me to actually meet people, share a discussion over coffee, and ``press palms" for a handshake, and workshops such as this are vital for promoting scientific contact and exchange of ideas.

I also want to mention a couple more impacts of the workshop on me. First, my colleague and collaborator Adrian Butscher also participated in the workshop, so this gave us a chance to discuss some possible avenues for research. We in fact are working on a project that was started at Stanford in the months after the BIRS workshop. Secondly, I was given the opportunity to present some of my work on the constraint equations; one result in particular I considered of minor interest, but I learned from one of the participants that the result was of particular interest to someone he knew; in fact, on my trip to Stanford in 2008, I had the opportunity to discuss this work at length with the other researcher.

Thank you once again for your hospitality at BIRS. I do hope very much to have the opportunity once again to attend a workshop in Banff (maybe next time in the summer!).

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David Brydges, Professor, Department of Mathematics, University of Mathematics

I have been to at least three workshops, one of which I organised. Scientifically speaking they were all very good experiences, but I often think back on: Statistical Mechanics of Polymer Models, May 10 - 15 2003. Because at that time I was a newcomer to Canada and it was such a pleasure to meet and to be welcomed by the UQUAM combinatorialists, in particular, Pierre Leroux. I immediately bought their book (Combinatorial Species and Tree-like Structures. Bergeron, F., Labelle, G. and Leroux, P) and later was a participant in their workshops in Montreal and started to meet them elsewhere as well, most recently at a special year in Cambridge. I greatly miss Pierre Leroux who died unexpectedly and am trying to complete a joint paper which he started. I doubt that I would ever have made these contacts if it were not for this BIRS meeting.

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Ron Livne, Professor, Department of Mathematics, The Hebrew University of Jerusalem

I have been to the workshop ``Number Theory and Physics at the Crossroads" which took place in September 2008 at BIRS. My stay was most helpful: together with Professor Noriko Yui we finalized our work on modularity of K3 surfaces with non-symplectic automorphisms (now submitted), and I had the opportunity to see what was being done in a very timely topic. I know I am not the only one to feel this way.

I hope the tradition of meetings at BIRS continues, it is of a very high value.

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Dmitry Jakobson, Professor, Department of Mathematics, McGill University

First of all, thank you very much for a wonderful atmosphere at Banff (which I visited for the first time this academic year).

I visited the Banff workshop 08w5092 Mathematical Theory of Resonances in October 2008. At the workshop, I started a joint paper with Frederic Naud (Avignon) titled ``Lower bounds for resonances of infinite area Riemann surfaces" which I wanted to write for a while but which got only finished after the workshop. We hope to submit the paper for publication this summer.

I also attended workshop 09w5040 Random Fields and Stochastic Geometry in february 2009, which was quite useful in another recent project in Riemannian geometry that I started. I will attend a related workshop at AIM at Stanford this august, and may organize something at CRM in Montreal in the following year.

Once again, thank you for a very nice atmosphere at Banff.

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Wilfrid Kendall, Professor, Department of Statistics, University of Warwick

Due to pressure of time, I have only been able to participate in one BIRS workshop (Densest Packings of Spheres, May 14 to May 19, 2005). However that was a great experience and mathematically most helpful for me. The area is tangential to my research but important; the quality and range of the presentations helped me immensely in forming a perspective on the state of current research in a difficult and intricate area. The excellence of the BIRS setup was also very important; it was possible for me to focus entirely on learning the topic without distraction.

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Andrei Kulikovsky, Professor, Institute for Energy Research - Fuel Cells IEF-3 (Research Center ``Juelich")

I have been visited Banff in March, 2005 for 1-week workshop on Fuel Cells Modeling. My impressions can be summarized as follows.

1. Scientifically the workshop was very useful and strong. There was a unique possibility to discuss the talks in detail.

2. Living together provides a great opportunity for intense communications. Some difficult scientific issues were discussed, which usually are out of the scope of ``normal" conferences.

2. Soon after this workshop I was invited to submit a chapter to a very prestigious book. This has definitely upgraded my position in the scientific community.

3. I have established good friendly contacts with many participants. The importance of these contacts is hard to overestimate; since 2005 they have been helping me to organize conferences, invite reviewers etc.

4. Last, but not least, these workshops definitely increase the prestige of Canada as one of the world scientific centers.

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Gaven J. Martin, Professor, Massey University, Director, New Zealand Institute for Advanced Study

I have attended two focused research groups at the Banff International Research Station for innovation in mathematics.

They both were excellent visits that built and then supported a sustained research programme that has resulted in a number of high quality research output (as measured by journal rankings in mathematics). These visits brought together a disparate group [from all over North America - together with myself from New Zealand] who previously had some links, but certainly not close, and who together were able to advance some of the more interesting research problems in the area. The collaborations initiated there have continued. I know that for some of the less senior researchers who were part of that group, these visits have been highlights of their early career and the results obtained among their best work.

The administrative support and the environment we met on our visits was superb and the staff were excellent.

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John Mason, Department of Mathematics and Computing, Open University & University of Oxford

I attended a meeting at BIRS concerning mathematics education. We met to gather and organise the fundamental concepts and constructs that would-be primary mathematics teachers need to encounter before they are set loose in the classroom, in order to be effective teachers of mathematics. The result was an extremely stimulating week. The discussions and ideas that came up were wide ranging and certainly opened up topics for deeper and further study. As it happens, I have recently been charged with writing a book on mathematics for primary mathematics specialists in the UK, and so I have been drawing upon the insights achieved during the BIRS week. The facilities and the opportunity they provide are outstanding and a significant contribution to the mathematical community.

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Andrea Malchiodi, Professor, Sector of Math and Analysis, SISSA

I visited BIRS a couple of times in the last three years (it was both times for workshops), and I have to say it was an ideal experience. The meetings were higly focused on my research interests and of excellent quality, so I had the opportunity to meet and interact with several colleagues. The enrironment is also extremely pleasant: the location and the structure are outstanding.

BIRS is now hosting several workshops every year, plus the research in teams program. This is making the Station one of the most well known places in the world where such activities can be carried out. I think it is very important for the mathematical community to have such a center at disposal, and I hope it might continue its activity in the future.

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Jan Conrad, Associate Professor, Fellow of the Royal Swedish Academy of Sciences Stockholm University

I participated in a workshop regarding statistical inference in cosmology and particle physics. In particle physics and cosmology with new vast amount of data to be interpreted in context of theories with many free ß parameters many statistical challenges are to be met. BIRS provided an unique environement for informal (thus very effective) discussions between experts in mathematical statistics and specialists in particle physics and cosmology. No doubt, the location and excellent facilities provided by BIRS attracted the top experts of both fields. The meeting resulted in what is known as the ``Banff challenge" which concerns a systematic comparsion of a number of statistical methods which were used in physics without proper motivation. For me personally, I started collaborating with a mathematical statistican, an expert in multivariate regression, a collaboration which pessimistically will result in a number of publications, but possibly mean a major step forward in the analysis of multidimensional theories.

A similar workshop at BIRS has been accepted for 2010. No doubt it is on the top of my priority list of workshops to attend.

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Jean Bellissard, Professor, School of Mathematics, School of Physics, Institut Universitaire de France

I have been a participant to several workshops at BIRS (may be 4 or 5), since 2005, I have been also an organizer once, I am a regular referee for the programs and I have been a member of the program committee once. I am a great fan of the BIRS even if I may be tough on evaluating the projects.

As a general fact, the center is very well organized in terms of accomodation, the food is usually appreciated by the participants, and the view offered at the restaurant is beautiful. The staff members in charge of the center, for the secretary, the coffee room and the accomodation, are all very kind, helpful and friendly.

And of course the place, in the middle of the Banff National Park is just gorgeous. Clearly the participants around me took a lot of pleasure to visit the park when it was possible.

On the scientific side, I have had the chance to be either in regular one week workshops with about 40 participants, or in focused research groups with 10-12 participants over a period of 1-2 weeks. In both cases, the conditions for work were ideals, because we did not have to bother about practical things and we could focus on the scientific results. I highly appreciated the effort made by the organizers to give a chance to the younger generation to talk and show their own work.

As an organizer, I realized that the strict limit made on the number of participants is actually forcing the committee to think seriously about who to invite instead of just invite the usual list of friends. It is actually a good thing. It is also important for the Scientific Committee to favor projects that put together people that usually do not talk to each others because they belong to different sub-communities.

But, as a professional, I did have a preference for the focused research groups in that the discussion was free and it was a fantastic way to learn a highly technical topic. The experience I had in 2005 and more recently in 2009 about the topology of tiling spaces was just outstanding. I suppose it was in the spirit of the early days in Oberwolfach when the small Bourbaki group was meeting. An intense experience during which everybody explains to his colleagues the subtelties of various aspects of the subject.

I am glad that the various funding agencies understood the role of such places in the propagation of knowledge among experts. It is necessary to exchange, more nowadays than in any other time, because the mean of communication and the increasing number of mathematicians over time everywhere in the world makes the exchange of information even more a crucial step for the efficiency of research. And even though the high technology allows to exchange fast, nothing has so far been able to replace the direct talk between people face to face. Nothing yet can replace a direct teaching on the board, in front of a small reacting public to spread the knowledge. Nothing can replace the discussion between people of completely different cultures to understand how their own intuition allows to turn around a difficult problem.

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Andy Ruina, Professor, Theoretical and Applied Mechanics, Mechanical and Aerospace Engineering, Cornell University

Some anecdotes:

I met Tadashi Tokieda at a Banff meeting. I had never heard of him before. Since then I have had a long correspondence, and invited him to Cornell and had many fruitful discussions.

My whole conception of the field of muscle mechanics was changed by two Banff meetings. I learned of, met, and learned from the key players in the sub-topic of my greatest interest. Such small single-track specialty meetings give one a sense of the field that you can't get at a big meeting.

Of course the setting is lovely, and the overall atmosphere and even the food, great.

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Dieter Happel, Professor, Department of Mathematics, Technische Universitat Chemnitz

Indeed, I participated twice in recent years in two meetings organized at BIRS. There I had the opportunity to meet several researchers I never met before and so had the opportunity to discuss mathematical problems of joint interest. Also having given talks at BIRS initiated and stimulated future research and though it is hard to know exactly but I am sure that some recent articles we inspired by the two stays at BIRS.

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Karl-Hermann Neeb, Professor, Department of Mathematics, Technische Universitat Darmstadt

Last year I took part in the

``Workshop on Quantum Affine Algebras, Extended Affine Lie Algebras and Applications'' in Feb. 2008

It was organized by Y. Gao and other colleagues.

This conference was full of inspiration for my work. Inspired by a talk of a colleague given on this conference, I wrote a paper on the ``classification of locally affine Lie algebras'' which is about to appear in the proceedings of this conference. I think that the result of this paper constitute an important advance of the theory of infinite dimensional Lie algebras which would not have come in existence without this conference.

I really appreciate the environment in Banff and the workshops organized there.

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Marcel de Jeu, Associate Professor, Department of Mathematics, Leiden University

I have attended a workshop in December 2006 which has a lasting impact on my research. The reason is twofold: I established many new contacts then, and I gained quite a few mathematical insights that would have been hard to obtain otherwise.

The facilities are eminently suitable for such workshops, as is the format that is used for the program. With sufficiently large breaks for lunch and dinner at these large tables in the dining room there is ample opportunity for informal contact (very important), and the same holds for the Common Room. The computer facilities at the bedrooms were most convenient.

When leaving I had no suggestions at all for further improvements, and I know from several Dutch colleagues that they have similar experiences. Even though it took me 20 hours to get from Leiden to Banff, it was well worth the trip and I certainly hope that I will have the opportunity to be there more often.

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Peter Kohl, Director, Cardiac Mechano-Electric Coupling Group, Department of Physiology, Anatomy and Genetics, University of Oxford

BIRS offers an internationally unique mechanism of research support, combining a unique setting with highly functional meeting, accommodation, and catering facilities. In terms of overall quality, the programme of the workshop I attended was among the absolute top events, on par with (or better than) Gordon Conferences. Certainly worthwhile the trip from Europe!

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Richard Hartley, Professor, Department of Information Engineering, Research School of Information Sciences

I attended a workshop on Computer Vision in 2006 at BIRS. I found this workshop particularly valuable. During the course of this workshop, I had the opportunity for lengthy discussions with Dr David Nister, one of the other participants of the workshop, now at Microsoft Research. These discussions led directly to a paper on the use of Galois Theory in Computer Vision, which was later presented at the IEEE conference on Computer Vision and Patern Recognition (CVPR) in 2007. This is one of the foremost conferences in Vision. The discussions at the workshop were of the utmost importance for the appearance of this paper.

Also, at the same workshop, I was particularly interested in talks by other participants Yuri Boykov who spoke of his work in Graph Cut optimization methods. I found this topic extremely interesting, and have subsequently begun to work and publish in this area myself.

I consider the BIRS workshops to be an excellent venue for research meetings. In my case, they were very valuable.

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Rocco Servedio, Professor, Department of Computer Sciences, Columbia University

I had a great experience in the workshop I attended at BIRS (on ``Analytic Methods in Computational Complexity"). There was an extraordinary roster of speakers. I took advantage of my visit to work with colleagues with whom I have longstanding collaborations, and was able also to start work on projects with researchers whom I hadn't collaborated with previously. Research I learned about at the meeting had a significant impact on one of the projects I was working on. All in all, I am very glad I could attend this meeting.

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L. Gary Leal, Professor, Department of Chemical Engineering, university of California

I have been to several BIRS programs over the years. The most recent was the workshop on ``Interfacial Dynamics in Complex Fluids", held in May 2006. This workshop was typical of what I have come to expect from programs at BIRS, well organized with excellent presentations, but much more!. There are several things that are unique about BIRS programs, and it is these aspects that make continued support of the Banff International Research Station extremely valuable for sciences in North America. First, the theme of this program was extremely timely (right at the beginning of the subject matter as an active research field) and unique in the sense that it would not have fit into the programming activities of virtually any other organization because it was so interdisciplinary and cut across so many fields. The programs that I have attended were also a nearly perfect size (I do not know if this is due to BIRS policies or is simply left to the workshop organizer); large enough to allow many of the principle researchers to attend, but still small enough to allow extensive communication and discussion outside the actual presentations (sometimes even during them). The residential setting is also perfect. With accommodations and meals shared by everyone, this contributes even more to the atmosphere of discussion and interaction that is really a hallmark of the BIRS programs. Of course, the setting in Banff is also a major plus; a special destination that draws many people to the BIRS programs and inspires us all in our moments of leisure. I view the BIRS programs as a special treasure that have played a very significant role in my own research. I would strongly lobby in favor of continued support. It would be a tragedy if this unique research conference and workshop facility did not continue to play the special role that it has developed in many branches of science and engineering research.

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Keith Ball, , Professor, Department of Mathematics, University College London

I am writing to express my strong support for the Banff mathematics conferences. There are only three or four institutes of its type in the world, holding one-week meetings in mathematics, almost every week, for a group of around 50 specialists. The others, at Oberwolfach, UCLA and AIM have rightly become some of the most famous and fondly regarded mathematics institutes anywhere. This format of short intensive meetings of experts is particularly useful in mathematics where large-scale experiments are less important than surprising juxtapositions of ideas. Canada has chosen very sensibly to support mathematics very strongly, perhaps because of the tradition embodied in the Fields Institute. The Banff centre is a vital part of that support.

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Sunil Mukhi. Faculty Member, Tata Institute of Fundamental Research

My participation in the BIRS activity ``Gauge Fields, Cosmology and Mathematical String Theory" from Feb 1-6, 2009, has been extremely useful to my professional career. This was an extremely high-quality meeting of leading experts in diverse areas mostly relating to String Theory as well as cosmology. I learned about many ongoing developments in the field from the talks. The fact that they were spontaneous and usually delivered on the blackboard was an added benefit, as also the fact that they tended to deal with ongoing and therefore unpublished research. The response to my own talk, including several suggestions for future work, was also extremely useful to me. This was my first visit to BIRS but I certainly look forward to many more such visits.

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Andrew Stuart, Professor, Department of Mathematics, Warwick Mathematics Institute

This message is written to indicate the highest regard that I have for the Banff International Research Station. Its organization and location make it a superb environment for small scale meetings, and small group activities; it is renowned the world over. Money spent on supporting research activities at Banff is well spent! I continue to be impressed with the choice of topics that have been covered at Banff in recent years, such as Molecular Dynamics and Data Assimilation, both cutting edge research areas for applied mathematics.

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Volodymyr Mazorchuk, Professor, Department of Mathematics, Uppsala University

I think the activities organized by BIRS are of very high quality and importance. My experience with BIRS is very good. I participated at one workshop organized a couple of years ago and this was very usefull as I learned quite a lot from the talks presented there and I made many new contacts and started several collaborations. I hope very much that BIRS will continue its activities.

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Steph van Willigenburg, Associate Professor, University of British Columbia

I would like to take this opportunity to reiterate what a powerful programme BIRS Research in Teams is, and to thank BIRS for the fantastic research opportunity, which allowed us to capitalize on ideas that had been formulated at the BIRS workshop ``Applications of Macdonald Polynomials".

My coauthors and I had an extremely productive week at BIRS and were able to prove a number of important theorems in algebraic combinatorics, which will form a groundbreaking journal article.

More precisely, we were able to prove generalisations of the famous Littlewood- Richardson rule that occurs in representation theory, algebraic geometry, and quantum computation.

This latter connection was particularly pertinent, as the concurrent 5-day workshop ``Quantum Computation with Topological Phases of Matter" gave our group a rare opportunity to interact with a range of mathematical physicists - not only during the lecture breaks, but also by attending relevant seminars, which they invited us to.

We would also like to praise the amenities provided by BIRS for our research. The two team rooms with large white boards allowed us to draw up substantial examples from which we were able to formulate our desired conjectures, and subsequently prove them. The rooms themselves also allowed the team to break out into subgroups to work on individual aspects of the proofs, so that we might use our time more efficiently and complete the project. The accommodation and meal facilities further augmented our abilities to concentrate fully on our research, as we did not need to waste precious time searching for either.

To conclude, I would like to thank BIRS for this invaluable opportunity, without which our project would have taken many more months, and perhaps years, to complete

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Henning Schomerus, Head, MEXT Nanoelectrophotonics, Faculty Member, Department of Physics, Lancaster University

This was an excellent workshop which brought together mathematicians, mathematical physicists and theoretical physicists. This event offered me an ideal platform to communicate my own research, which resulted in a new and successful collaboration with one of the main organisers. A long two-part paper been submitted recently (see arXiv:0906.0891 and arXiv:0906.0892).

The facilities and local organisation at BIRS are excellent, and I am looking forward to attend similar events in the future.

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Fouad El Zein, Professor, Department of Mathematics, Universite de Nantes

As a participant of the meeting in Hodge theory April 6-11 in 2008, I had the opportunity to renew contacts with mathematicians in North Americain the field. The discussions, I had encouraged me to write a new proof of the purity and decomposition theorem in general beyond my conference in the isolated singularity case.

There also we formed an organization committee of a conference in Hodge theory and Shimura varieties at ICTP which has been just approvedfor summer 2010 June 14 - july third.

The Banff International Research Station has been fulfilling his aim and has become a well known center in Mathematical Sciences.

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Fredrik Manne, Professor, Department of Informatics, University of Bergen

I attended a Banff workshop in 2005 on ``Self stabilizing algorithms". Being new to this community the workshop gave me a great opportunity to make connections and interact with the other more experienced researchers. The relaxed atmosphere (and beautiful surroundings) created a very good environment in which to work. Based on the contacts I established at Banff I have since published two papers and attracted funding for international collaboration. One of my PhD students also later got an opportunity to go to a 6 month stay with one of the organizers at the Banff workshop.

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Jon Keating, Professor, JP Keating FRS, Department of Mathematical Physics and EPSRC, School of Mathematics, University of Bristol

I participated in the BIRS workshop 07w5114 (July 8 to July 13 2007).

My experience at Banff was exceptionally positive. The atmosphere was relaxed but serious; the surroundings were wonderfully stimulating; and the Centre was a model of efficiency.

I met several researchers I had not previously encountered at the Workshop and learned some new and exciting things.

I left the Workshop with several new ideas and have pursued these with my colleague Dr Nina Snaith and a PhD student vigorously since then. I am very proud of what we have achieved. Specifically, we have found a way to model the statistics of the zeros of elliptic curve L-functions that explains some very puzzling data presented at the BIRS Workshop by Steve Miller.

BIRS is, in my experience, unique in the way it runs week-long focused workshops. These play a most valuable part in the international research endeavour.

I was so stimulated by the Worshop I attended in 2007 that I have recently proposed a Workshop myself and would be delighted to visit Banff again.

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William Meeks, Professor, Department of Mathematics, University of Massachusetts

I attended a geometry conference at Banff in December, 2007. At the conference I made many new contacts and had an exciting time at the Banff conference center. As a consequence of my attending the conference, I ended up visiting a couple of other places. One invitation I received was to give 9 lectures at a conference at KIAS in Korea. I look forward to attending another productive conference at the Banff center sometime in the future.

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Etienne Sandier, Professor, Department of Mathematics, Universite Paris

I participated in a workshop at the Banff International Research Station (BIRS) in 2006. It was a meeting of very high scientifical interest which gave me awareness of some important trends in research in the field of nonlinear partial differential equations. Very concretely, there are papers i read and talks i attende to this day which i wouldn't grasp if i had not attended this workshop. I think that such workshops, if their program is well conceived as it was the case at BIRS, are great because they give the opportunity to get into contact not only with one person's research, but with a whole field and its facets.

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Alexei Skorobogatov, Professor, Department of Mathematics, Imperial College London

I participated at the workshop in December 2008 called ``The arithmetic of K3 surfaces", which I also co-organized. There we met again with Prof Yuri Zarhin (Penn State), and started working on another joint paper. I am very excited by this new work, and other work that was made possible by our results, because we solved one of the open questions discussed at the Banff meeting. We found a way to compute the geometric Brauer group of Kummer surfaces, and used this in another paper to give examples of diagonal quartic surfaces over Q with trivial Brauer group, and also to produce a bound for the size of the Brauer group of these surfaces over Q.

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Jan Stienstra, Professor, Department f Mathematics, Utrecht University

I attended workshops at BIRS in 2003 and 2006, both organized by prof. Noriko Yui (and others). The one in the review period was Workshop 06w5041, Modular Forms and String Duality, June 3-8, 2006. At this workshop I gave two separate lectures. The first lecture on ``dimers and hypergeometric functions" was a report on research done over a period of several years before this workshop. This research matured further while I was writing my paper for the proceedings of this workshop (Fields Institute Communications vol 54, p.125-161). After receiving reactions to this paper I could complement my research with some striking applications of the dimer constructions, which led to two further articles and several invitations to conferences. My second talk at Workshop 06w5041 was an informal lecture about my ongoing work with Don Zagier about ``bimodular forms and the holomorphic anomaly equation" and was related to Bouchard's talk about his work with Klemm on ``the holomorphic anomaly equation". The workshop also gave Zagier and me a good opportunity to work on our project and to discuss this with Klemm and Bouchard.

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Cecilia Salgado, Research Assistant, Université Denis Diderot- Equipe Théorie de Nombres

I participated at the workshop on K3 surfaces held at BIRS on december 2009. It was one of the best, if not the best, conference I have ever been to. Not only because the organizers put a lot of effort on it, but also due to the wonderful conditions of work at the BIRS.

The BIRS presents the perfect environment to research since it's calm and its staff is amazingly efficient and friendly. I saw myself free of any worry or inconvenience at BIRS and had a full week dedicated to my research: which certainly doesn't happen in my day to day life.

I'm looking foward to another conference at BIRS.

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Rolf Kötter, Professor, Chair, Section Neurophysiology & Neuroinformatics at the Donders Institute for Brain, Cognition and Behaviour, Radboud University Nijmegen

I'm writing to say that my stay at BIRS was most enjoyable both on the scientific and on the personal plan. Although the experience is only two weeks old I can already say that it will be inspiring further such meeting. Together with some participant I am currently planning a research project that otherwise would not have taken place.

BIRS and Banff are excellent places for encouragement of scientific creativity. Hopefully it will stay like this in the future. I wish it gets even better...

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Cristian Giardina, Assistant Professor, Department of Mathematics and Computer Science, Eindhoven University of Technology

I did not have yet the chance of attending a workshop at BIRS . However I am organizing a one week workshop [Statistical Mechanics on Random Structures, 09w5055] together with P.Contucci, F. Den Hollander, A. Bovier to be held on November 2009. Form the enthusiastic responses to invitations to our workshop I understood that BIRS has made a reputation among scholars as a unique place with interesting thematic meeting. I look forward to visit BIRS in the fall.

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Dan Segal, Professor, Department of Mathematics, University of Oxford

I was a participant in the ``Geometric and Asymptotic Methods in Group Theory workshop" at BIRS in June 2005. This was a valuable as well as enjoyable experience. The workshop brought together leading mathematicians from Europe and America, several of whom I had not met before, and gave us the opportunity to learn from one another. I can't remember any specific results that came out of this process, but it certainly helped my thinking to develop in certain directions.

The setting is fantastic and undoubtedly helps in attracting participants from far and wide. I wish you every success in continuing this excellent facility.

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Chad Schoen, Professor, Department of Mathematics, Duke University

I have attended one BIRS workshop in the past 4 years. It was very helpful. I'm quite isolated at my own university, so it was very helpful to get to meet so many workers in the broad field of arithmetic algebraic geometry. My own field is more classical algebraic geometry, but I benefit greatly by learning the arithmetic side of the subject and have used some arithmetic techniques in my work. The specific focus of the meeting I attended was on K3 surfaces. Some of what I learned at the conference relates to work I am presently doing. The fact that the conference gave me a nice overview of a specialty in which I am not very knowledgeable, but which is highly interesting and not far from the work I do, was very valuable.

The format of the program was very good. I attended all the talks, which is not something I usually do at conferences. Also I had many valuable mathematical discussions with participants. I learned more than at most conferences. I think that this is in part due to the way the facilities are set up at BIRS. There is more time and opportunity to interact and to meet new people than at many conferences, especially those held at a site in a large city, where people tend to scatter when not attending a lecture.

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Denis Auroux, Associate Professor Department of Mathematics, Massachusetts Institute of Technology

I just wanted to mention one instance where a visit to BIRS significantly impacted my research:

During my recent visit to Banff for the workshop ``Interactions of geometry and topology in dimensions 3 and 4" (March 22-27, 2009), I attended a very enlightening talk by Dylan Thurston about his recent work with Lipshitz and Ozsvath on ``bordered Heegaard-Floer homology", which led me to become actively involved in this topic and study the connections between Ozsvath-Szabo's low-dimensional topological invariants and the symplectic geometry of symmetric products of Riemann surfaces (in particular, Fukaya categories). In the process I found an interesting alternative description of their construction - a picture-perfect instance of an unexpected result coming out of the interaction between different groups of mathematicians.

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James D.E. Grant, Professor, Department of Mathematics, Universitaet Wien

I attended a Focused Research Group meeting (The Xi-transform 07frg138) at the Banff Internation Research Station from March 25th until April 1st 2007.

I found my visit to BIRS extremely rewarding for several reasons. Firstly, I attended along with seven other academics from various academic institutions, most of whom I did not know previously. It was therefore an opportunity to make contact with mathematicians working on related topics. (In addition, in this regard, I had several rewarding conversations with people attending other meetings at BIRS that were running concurrently.) Secondly, I found the tranquil setting of the centre very conducive to the ``clarity of thought" required for mathematical research. The high quality organisation and the compact nature of BIRS meant that one was free to concentrate on research, rather than the mundane banalities of everyday life.

There were several direct scientific outcomes related to my visit to BIRS. Firstly, M. Dunajski and I completed the final version of our paper ``Multidimensional integrable systems from deformations of Lie algebra homomorphisms" (joint with I.A.B. Strachan), which has now been published in the Journal of Mathematical Physics. In addition, based upon work that I presented in my talk at BIRS, I had conversations with M. Dunajski concerning the possibility of finding projective structures on hyperbolic monopole moduli spaces. This is expected to be a direction for future collaborative research. Moreover, based upon remarks of B. Doubrov after the talk of M. Dunajski, I became aware of the work of Grossman concerning the connection between anti-self-dual conformal structures of split signature on four-manifolds and equivalence classes of pairs of second order ordinary differential equations under point transformations. Finally, I have several interesting conversations with B. McKay and A.R. Gover concerning exterior differential systems. Dr. McKay, whom I had not met previously, has since invited me to University College Cork as a Colloquium speaker.

To summarise, I found my visit to the Banff Internation Research Station very valuable, both for my personal research and for making new contacts within the mathematical community.

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Marius Junge, Professor, Department of Mathematics, University of Illinois

1) Quanhua Xu and myself participated in the research in pairs program at Banff approximately 5 years ago. The results of this collaboration have just recently been accepted in Inventiones, as you know a very highly ranked journal. Yesterday we discussed how, apart from reports, we can express the fact that the foundation of all that work has been put into place at Banff. By the way, our competing team solved their problem within a few days. 2) There will be quantum information theory conference next week in Toronto. This conference is a follow up of a workshop on a similar topic organized by Kribs and Ruskai. It brings together researchers in quantum information theory and operator spaces, groups which usually don't interact to much if it were not for the workshop organized at Banff.

Of course, this are just individual examples of successful programs running at Banff. But the sum of all these `little successful events' makes Banff such an important resource for research in mathematics.

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Rama Cont, Associate Professor, Columbia University

I attended in 2004 a meeting on ``Semimartingale theory and application" at Banff International Research Station, organized by the Pacific Institute of Mathematical Sciences. This week-long research workshop brought together an excellent group of researchers and doctoral students from Canada, the US, Europe, Australia and Asia. The convivial environment of BIRS and the format of the workshop allowed all participants to have extensive discussions and initiate contacts and new projects and for doctoral students to have access to international experts during a whole week. My impression was that Canadian researchers in particular greatly benefited from this and others BIRS events to gain exposure to international research in their area.

This meeting resulted in new collaborations for me and two subsequent research papers I have written with participants of the conference were initiated at this event.

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David Garfinkle, Professor, Department of Physics, Oakland University

The 2005 BIRS workshop on numerical relativity was where Frans Pretorius first presented the solution of the two black hole problem. This problem, the accurate and stable simulation of the collision of two black holes and of the gravitational waves that such a collision produces, has been the main focus of research in numerical relativity for the last two decades. Before Frans' result, computer simulations of colliding black holes had been unstable, and no physics results could be found using them. Spurred by Frans' success, as presented at BIRS, other groups subsequently perfected their own approaches to the problem and were able also to perform successful simulations of colliding black holes.

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Vlastimil Krivan, Professor, Department of Mathematics, University of South Bohemia, Chair, Department of Theoretical Ecology, Biology Center, Chair, Department of Mathematics and Biomathematics

In 2006 I participated in workshop ``Evolutionary Game Dynamics'' organised by the BIRS. This was also how I learnt about BIRS. I want to express my deep admiration about exceptional good organization and profound success of this workshop. I have no doubts that the other activities organized by BIRS are as successful as this one.

Evolutionary game dynamics are used mostly by two quite distinct group of people: economists and mathematical biologists. The importance of this meeting was that it brought together both groups that would otherwise did not meet at regular conferences and other meetings. Yet, mathematical methodology for both groups is the same so it was very good these two groups could interchange their ideas. Moreover, location of BIRS is very good for people to meet and talk, that is very important for their future collaboration. As a result of this meeting, besides giving talks, with other two participants we wrote an article during the meeting that was published shortly after the meeting in a leading ecology journal. This would not happen without the BIRS meeting!

In general, I believe that activities such as the BIRS center should be continued because this is a very effective way of supporting science. The success relies on the fact that the meetings are well focused, well planned, and the BIRS provides an excellent environment that attracts best people to come.

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Yan Soibelman, Professor, Department of Mathematics, Kansas State University

I participated in the workshop ``Tropcal Geometry" at BIRS few years ago. I found the activity,organization and environment very stimulating. I think that BIRS conferences play in North America the role similar to the one Oberwolfach conferences play in Europe. In this sense it is unique. I am pretty sure that the impact of BIRS on the level of research both in Canada and US is very big.

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Tim Cootes, Professor, Computer Vision, Imaging Science and Biomedical Engineering, University of Manchester

I was lucky enough to attend a meeting on Mathematical Methods for Medical Image Analysis at BIRS in November 2007. The meeting drew together many of the leading experts in the field, giving them the opportunity to become acquainted with each other's most recent work, to share ideas and consider where the field was going. It was a very rewarding experience, allowing me to meet new people and old colleagues in a relaxed atmosphere and to concentrate on the research without outside interruption. For me, it lead to a deeper understanding of current methods and gave me a chance to think about future research directions. BIRS is a tremendous facility which is a credit to its staff and to those who fund it.

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L.C.G Rogers, Chair, Statistical Science, University of Cambridge

I visited in May 2006, and found the conference I attended there to be one of the most interesting I went to in the last 10 years. It allowed me to meet up with colleagues working in contract theory, an area that I have since developed interests in, largely as a result of this initial exposure - keep up the good work!

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Mark de Cataldo, Professor, Department of Mathematics, Stony Brook University

I have participated in the Hodge Theory workshop in Banff in April 2008. It was an excellent conference. I wad exposed in a short period of time to the newest and best results in the field. The atmosphere was very conducive to mathematics discussion of which I had many. Some of these discussions have been very useful in my current research on the Hodge theory of character varieties. I really hope to participate in future events of this caliber.

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Andrew Read, Professor, Department of Biology and Entomology, Pennsylvania State University

I was at a Biomath course in May 2009 (MITACS Summer School, The Mathematics of Evolution and Invasions in Ecology and Epidemiology) as a speaker. Two things really struck me. First, the motivationally high level of conversation with the other Faculty - excellent people from US, Canada and Europe. Second, the impact it had on the students. Several have been in touch with me since proposing projects.

And perhaps of more immediate benefit, I have struck up a collaboration with one of the faculty I'd never met before. He is bringing new statistical tools to bear on our experimental data of 15 years. I am seeing things in the data I had not seen before, which seem likely to profoundly impact the way we publish for years to come.

At the meeting, I also got some work done with an existing collaborator - which also opened my eyes to a whole new vista.

Oh, and I got in an excellent afternoon's trip in the mountains.

An absolutely excellent meeting in an excellent venu.

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Alard Roebroeck, Department of Cognitive Neuroscience, Maastricht Brain Imaging Centre (MBIC), Maastricht University

Attending a 5-day workshop event at the BIRS as a participant has been an outstanding and productive experience. The atmosphere of creative collaboration in the Banff Centre in general and of scientific communication at the BIRS specifically was very stimulating. The facilities offered at BIRS are highly conducive to small meetings of specialized scientists focusing discussion on specific problems and developments in their field that otherwise would not take place. The more common larger conferences just do not offer this opportunity for extended multi-day discussions among a small to medium sized group of specialists. The extended provisions for workshop participants are very helpful, especially for young seniors and post-doctoral researchers that often do not yet have grant money to cover costs of registration, accommodation and food normally attached to conference participation. During my stay at BIRS I have made new contacts in my field of expertise and been able to start new collaborative projects with international colleagues. The talks and discussions I have attended have really made a difference in setting out directions for my future research.

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Daniel Weiskopf, Professor, Department of Computer Science, Universitat Stuttgart

I attended the BIRS 2004 Workshop on ``Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration".

I very much enjoyed this workshop, with extremely open and productive discussion, as well as fruitful new collaborations established there. I think that BIRS is the only place worldwide besides Dagstuhl that fosters in-depth discussions between researchers in the interdisciplinary area between computer science and mathematics.

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Aad van der Vaart, Professor, Department of Mathematics, VU University Amsterdam

From April 5-10 2009 I had the pleasure to participate in the workshop Semiparametric and Nonparametric Methods in Econometrics 09w5032 at BIRS. The workshop brought together researchers from statistics and econometrics, two fields that have a large border, but whose contributors do not meet at regular conferences. It was very enlightening to hear how econometricians look at semiparametrics and which problems have come to the forefront in the last couple of years. The new perspective will certainly influence my future research programs. It was also useful to present my own research to a new audience. The strengthening of personal contacts with a few of the participants whom I had met only a couple of times before, and meeting others whom I only knew by name, will benefit future research.

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Anthony Brockwell, Associate Professor, Department of Statistics, Carnegie Mellon University

The BIRS workshop I attended was one of the most useful (and memorable) workshops in my academic career.

The group of people working in my primary area of research is spread widely around the world, with significant portions in the US, UK, France, Canada and Australia. Therefore I tend to interact mostly with the small subset of this group who I know best. Partly because of the spectacular setting at Banff, and partly because of the reputation of BIRS (and our workshop organizers), the Monte Carlo methods workshop I attended brought a lot of these researchers together. As a result, I made a number of new connections with researchers in my field. Furthermore, the workshop itself was one of the most intensely active forums for the exchange of good ideas that I have experienced.

On a side-note, the workshop also sticks out in my mind because the food was very good. Many conferences in the U.S. provide nothing more than bad coffee and stale bagels, but BIRS provided meals that we genuinely looked forward to. Although it shouldn't matter so much, I found that a significant amount of workshop discussion took place between participants over breakfast.

Anyway, to summarize, the BIRS workshop I attended had a lasting positive impact on my academic career. I believe BIRS reflects in an enormously positive way on the Canadian scientific community, especially internationally, since it is well-known (and considered a highly-desirable workshop location) to non-Canadian researchers. I wish you the best of luck with your new proposal.

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Neil Dummigan, Department of Pure Mathematics, University of Sheffield

I attended the BIRS workshop ``Modular Forms: Arithmetic and Computation", June 3-8, 2007. My paper ``Rational points of order 7", Bull. London Math. Soc. 40, no. 6, 1091-1093, was a direct response to a question posed by a fellow participant during an informal conversation at the workshop. The high quality and quantity of the food meant that communal meals were very well attended, and this made the workshop especially good for making and renewing contacts and having informal discussions. The beautiful surroundings were very conducive to quiet reflection.

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Andrew J. Majda, Morse Professor of Arts and Sciences, Department of Mathematics and Climate, Atmosphere, Ocean Science (CAOS), Courant Institute of Mathematical Sciences, New York University

I have been an organizer and main participant in two BIRS workshops in the last three years. The set-up at BIRS, both physically and organizationally is the best one in the world for interdisciplinary focused workshops with extensive relaxed discussion of major science problems. I have benefited substantially in my own research perspective through these workshops; as an organizer, I routinely have heard comments such as ``the best workshop, I've attended." I eagerly look forward to my next opportunity to participate in a BIRS workshop in applied mathematics interacting with climate science!

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David Odde, Professor, Department of Biomedical Engineering, University of Minnesota

I have been to many scientific meeting venues in North America and Europe and BIRS is THE best I have been to in my 14 years as a professor. The facilities and environment are outstanding for scientific discussions. I always look forward to meetings there!

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David Cox, Professor, Department of Mathematics, Amherst College

I attended one workshop at Banff, maybe in 2004 or 2005. It was a commutative algebra workshop, and I remember that Juergen Herzog, Winfried Bruns, David Eisenbud, Alicia Dickenstein and Joseph Gubeladze were there. I have one story from my visit that may be of interest.

I am an algebraic geometer, not a commutative algebraist, so I was slightly out of my element at the workshop. This was actually good, since I had some commutative algebra questions arising from work I was doing with the geometric modeling community. In geometric modeling, the method of moving curves and surfaces was pioneered by Sederberg and Chen, and in the curve case led to the useful notion of a mu-basis. In the surface case, it was known that homogeneous mu-bases can't exist, but the existence of affine mu-bases was an open question. I gave a talk at Banff that touched on this question, and in discussions with Bruns and Herzog after the talk, it became clear that the existence of affine mu-bases for surface parametrizations in 3-space is a consequence of the Serre conjecture that locally free sheaves on affine space are free. This led to the paper ``The mu-basis and implicitization of a rational parametric surface" (J. Symbolic Comput 39 (2005), 689-706, written with Chen and Liu) that proved for the first time the existence of affine mu-bases, an important result in geometric modeling. This would not have happened without the Banff workshop that I attended.

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Ahmed Sameh, Professor, Department of Computer Science, Purdue University, College of Sciences

I am glad to state that I attended a workshop at BIRS on ``Model Reduction" that resulted in great collaboration among four universities, one of them in Belgium, and also funding from the U.S. National Science Foundation. In addition, I enjoyed very much the surroundings and the overall environment that facilitated interaction among my fellow scientists at the meeting.

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Judy Martin, Education Mentor, Galileo Educational Network

I have been involved with BIRS for the past four years through the Galileo Educational Network. Each and every time I have been part of the conferences it has been a profound experience. The intensity, the program and the professional that are part of these conferences not only enhance, support and further the work that myself and our organization work with but that of the teachers and colleagues that we work with. It has significantly moved the work that we do in mathematics to a whole new level. The collaboration with Ted Lewis, Andy Lui and others has brought new insights in order to support the work we do with teachers. Each year we bring new teachers that we have directly worked with and they too have foudn the experience insightful and helpful for them once the go back to their classrooms. Involving the scientific community would indeed enhance the BIRS experience.

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Juan C. Migliore, Associate Chair, Professor, Department of Mathematics, University of Notre Dame

I have attended three workshops at BIRS, in 2003, 2006 and 2007. The set-up that you have built is an excellent one for both the creation and the dissemination of mathematical research results. The ability to see a carefully selected group of researchers in my area, to listen to talks about their recent work, but at the same time to have plenty of time (and blackboards) to talk to them, and to meet with colleagues with whom I am collaborating, has certainly led to, and improved upon, several of my papers.

I would like to describe just one of these, which took place at the workshop ``Syzygies and Hilbert Functions," October 14 to October 19, 2006. Craig Huneke approached Uwe Nagel and myself to tell us about some work he had in progress with Bernd Ulrich. Since my grad student days, I had always been interested in the question of whether minimal linkage would always lead to minimal elements in a linkage class, and in a recent paper Geramita, Harima, Shin and I had made a comment about a specific counterexample, but it did not have a proof. Huneke and Ulrich had found a way to tweak that example and thereby give a very nice approach to showing that this really was a counterexample, the first one known. Nagel and I were very interested, and we talked extensively about it and found a way to make a nice class of examples, based on what Huneke and Ulrich had done. We approached them, and agreed to put it all together in one paper. It is inconceivable that this paper would have come about without our time at BIRS. Furthermore, about a year later, Nagel and I saw a way to extend this work in several directions, so that now the issue is really largely settled in all interesting directions that I can see (sometimes the answer is yes, sometimes it is no). So the time at BIRS not only led to one paper, but it set the stage for a subsequent paper. I'm really proud of both of these papers.

I truly hope that the grant for BIRS will be renewed. BIRS is a very valuable asset to the mathematical research community, and it is certainly at least on an equal footing with any other research center in the world with similar goals. (I have been to Oberwolfach and to Luminy, for example.)

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Samuel Petite, Researcher, MaĒtre de Conférences, Department of Mathematics, Université de Picardie Jules Verne

I am a mathematician and I give here my experience of my stay in Banff during five days. The Banff center gave me the opportunity to work on my research, discuss with my colleagues of the same topics that I can not meet the rest of the year. I should precise that specialist are distributed almost everywhere in the world. I did not have to look after the lunch or my standard teaching or administrative tasks : only work on research. This is a priceless time for a researcher. Moreover, this advantage is also true for everybody in the meeting, at the opposite of meetings organized in a university, where the locals have always administrative and teaching time.

More than just a meeting to present some new results, the visit in Banff gives the opportunity to share questions, intuitions and direction in our topics. In my experience, I can not quantify a number of paper or theorem that I made or will make thanks this stay. It gave me essentially interesting possibility of results in our topic. In a concrete way, this stay enabled me (and colleagues) also to well prepare an ask for a 300 kŘ funding (French ANR), which we have finally obtained. Such funding is not obvious to obtain without a scientific high level and a precise goal based on a diversified researcher's team. Thanks the meeting place of Banff, we have well coordinate such heavy project.

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dun Reiten, Professor, Department of Mathematics, Norges Teknisk-Naturvitenskapelige Universitet

I have participated in 2 Banff conferences, the first one in the fall ot 2005, organised by Colin Ingalls etc on noncommutative geometry. It was a very interesting conference. And in addition Bernhard Keller and I had very useful conversations leading to a very popular research paper, which last year was selected as a ``fast breaking paper in mathematics." Also, the second conference last September was quite interesting, organised by Helmut Lenzing etc. [BIRS] is very useful for the mathematical community and I hope that it continues.

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Rick Durrett, Professor, Department of Mathematics, Cornell University

I have attended a couple of meetings at BIRS, worked on a research in teams for two weeks, and I am the organizer for a meeting Sept 6-11, 2009. The research in teams experience allowed Ed Perkins, Leonid Mytnik, and I to come together in the same place and finish a paper that had been stalled for some time since Leonid is in Israel, I am at Cornell, and Ed is at UBC.

Banff provides a wonderful setting for conferences with the shared meals and accomodations making informal conversations outside of the lecture hall easier than at a normal conference where people stay at different hotels. The staff has made the organization of our meeting quite easy and we are looking forward to a stimulating exchange of ideas between mathematicians and biologists.

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Peter W. Glynn, Professor, Department of Management Science and Engineering, Stanford University

I participated in a BIRS workshop in October of 2007 on the connections between dynamical systems, information theory, and Lyapunov exponents. It was a very stimulating workshop, as I was introduced to researchers studying methods very different from those I have been pursuing in the Markov process/iterated random function setting. In particular, I now am involved in regular discussions and a likely collaboration with Tsachy Weissman, who comes into this area from the perspective of information theory. The BIRS workshop was a critical ingredient in generating this collaboration.

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Gary McGuire, Associate Professor, School of Mathematical Sciences, University College Dublin

I attended a workshop on Polynomials over Finite Fields in November 2007 at BIRS. I found this workshop extremely useful to me in my research. At the workshop I began a collaboration with John Dillon which resulted in a joint paper. I found the whole environment and facility very helpful in fostering conversations between researchers. I think everyone got a lot out of the workshop.

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Eric Darve, Professor, Department of Mechanical Engineering, Stanford University

I organized the BIRS Workshop 08w5074 last year. The workshop was a fantastic success. BIRS was most helpful. With the accommodation, food, etc, already in place and the administrative support, the workshop was very easy to organize and went very smoothly. There was an excellent atmosphere, especially in the common room where several interesting scientific discussions took place. The place itself, Banff and the national park, are excellent. Overall this was a very useful workshop scientifically and really helped create long lasting bonds and relationships between researchers.

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Haiganoush Preisler, Research Scientist, Pacific Southwest Research Station

I have attended two conferences/workshops at Banff in the last 4 years. Both times my experience there was one of the most important in my professional career. Although you meet colleagues from around the world in other conferences, there is no substitute for being able to spend a longer time (usually a week) with a handful of colleagues that are all working and concentrating on one topic, and to do so in such idyllic and calm surroundings. My experience at Banff has led to many collaborations, in particular with my Canadian colleagues, working on new statistical methodologies necessary for the study of fire prediction and the interactive effects of fires and insects on Climate related issues. The new methodologies have been necessary as new data types are collected, whether from satellite imagery or from GPS telemetry or from process-based simulation models. Almost all the papers relating to statistical issues of these topic in the last few years have been mainly by the group that assembled at Banff or with collaboration with at least on of the participants at those workshops. When we first started, the use of these statistical methodologies in the field of fire research was very rare. Lately, I have noticed it has become main stream and are used regularly in most of the applied papers I read or review.

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Bernard Brooks, , Associate Professor, Assistant Head, School of Mathematical Sciences, Rochester Institute of Technology

I quite enjoyed my time at the research station. The meeting there allowed me to interact with researchers whose suggestions and critiques have made my research stronger. As well, some of the new contacts that I made there still provide that research feedback as well as friendship. One of the strengths of the BIRS is that none of the researchers at the meeting were on home turf. We were all immersed together in an nonurban environment for the entire stay. This allowed our ideas to take shape, to gel. There were no distractions or interruptions from any issue normally found in the foundation of Maslow's pyramid so we could focus on the pyramid tip. Not only do I hope this centre continues, I hope it is replicated so that more researchers can benefit.

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M. Gregory Forest, Grant Dahlstrom Distinguished Professor, Departments of Mathematics & Biomedical Engineering, Co-Director, Institute for Advanced Materials, Nanoscience & Technology, University of North Carolina at Chapel Hill

I attended a very impressive workshop on Complex Fluids at BIRS. The workshop was organized by James Feng and a couple others, and it brought together a diverse group of experts as well as junior scientists and mathematicians. The format was stimulating, and I met people there that I do not think I would have met otherwise. More importantly, I was able to actually TALK to people in a way that almost all professional meetings do not allow. One of the coattail effects is that I developed relationships that have continued, I hired one of my best-ever postdocs through someone I met there, and I continue to see some of the participants at international meetings of major societies. The BIRS reminds me very much of MSRI at UC Berkeley in its nascent phase, which I was privileged to participate in. Congratulations on a wonderful research enterprise.

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Anthony Bloch, Collegiate Professor, Department of Mathematics, University of Michigan

I have enjoyed two wonderful visits to the Banff Research station - one for a workshop on nonholonomic mechanics and another on geometric mechanics. I have profited from and really enojoyed these workshops. These visits were immensely helpful in inspiring my work on nonholonomic mechanics and quasivelocities with Marsden and Zenkov. I also met other excellent people in my field such as Larry Bates who I would not normally see.

I hope very much to see the station continue.

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Michael Kozdron, Associate Professor, Department of Mathematics and Statistics, University of Regina

I am writing to express my support for the Banff International Research Station and to explain how my professional experiences at BIRS have made a difference in my research and scientific work. I have been fortunate to participate in two BIRS workshops, ``Critical Scaling for Polymers and Percolation" in 2005, and ``Recent Progress in Two-Dimensional Statistical Mechanics" in 2008. When I attended the first workshop I had only recently completed my Ph.D. and so it was very important to me that the other participants included both younger researchers and senior leaders in the field. I was able to learn about the important trends in the field from senior leaders and to forge research links with other junior researchers who shared similar interests. Furthermore, my paper ``On the scaling limit of simple random walk excursion measure in the plane" (ALEA Lat. Am. J. Probab. Math. Stat., 2:125-155, 2006) was completed during this workshop. The support of BIRS is explicitly acknowledged in the published version. When I attended the second workshop in 2008, I was invited to present a lecture on my recent work and I am thankful to the organizers for that opportunity. Finally, I co-organized a research-in-teams meeting on ``The Rate of Convergence of Loop-Erased Random Walk to SLE(2)" in August 2008. This was an extremely valuable experience. BIRS provided the financial support to enable three young researchers from disparate locations, Regina, New York, and Stockholm, to meet in person for a week and collaborate on a specific project. The net result of our week at BIRS was that many technical arguments were outlined and a first draft of a paper was started. Currently, we are finalizing the paper and plan to submit it for publication very soon. The BIRS facilities were crucial to the success of our collaboration.

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Paul Monsky, Professor, Department of Mathematics, Brandeis University

In recent years I've twice been to Banff for commutative algebra workshops. Apart from the pleasure I've had in getting to know people like Anurag Singh and Hailong Dao there have been interesting mathematical consequences. On the first occasion I met Nobu Hara and our discussions resulted in one of the first papers on the discreteness and rationality of F-jumping numbers. The second time I came to Banff I got to know Holger Brenner, and shortly thereafter we settled the localization problem for tight closure in the negative. In both cases these were problems rather removed from my specialty, Hilbert-Kunz theory, and I was very pleased that this exotic theory could have applications of a more general interest. Conversely I spoke to algebraic geometers at the workshop about a conjecture of mine about characteristic 2 nodal plane cubic curves. If they succeed in proving it, there will be remarkable consequences for Hilbert-Kunz theory. This hasn't yet happened but the workshop gave me a chance to spread the word, and I remain hopeful.

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Linda J. S. Allen, Professor, Department of Mathematics and Statistics, Texas Tech University

In the past 5 years, I have been fortunate to participate in three different BIRS activities. In each of these activities, I have given presentations to faculty, students, and other research personnel, as noted below:

``An Introduction to Stochastic Epidemic Models-Parts I, II, III", PIMS-MITACS-MSRI Special Program on Infectious Diseases Summer School, June 19-27, 2004.

``Emerging Wildlife Disease Modeling". Workshop on Mathematical Epidemiology. August 20-25, 2005.

``Stochastic models of invasions and epidemic", 2009 Summer School on The Mathematics of Invasions in Ecology and Epidemiology, May 10-17, 2009.

The summer school in 2004 led to a book edited by F. Brauer, P. van den Driessche, and J. Wu, Mathematical Epidemiology, Lecture Notes in Mathematics, published by Springer in 2008. My contribution was Chapter 3, An Introduction to Stochastic Epidemic Models.

The workshop in 2005 provided an opportunity for Pauline van den Driessche and I to collaborate on stochastic epidemic models, extending some earlier work of P. van den Driessche and colleagues to a stochastic setting. This work was published:

Allen, L. J. S. and P. van den Driessche. 2006. Stochastic epidemic models with a backward bifurcation. Mathematical Biosciences and Engineering. 3(3): 445-458.

The summer schools and workshops have been some of the high points in my teaching and research career. The participants in these activities are eager and enthusiastic. During the five to seven days of the workshops, there are opportunities to talk with participants in an informal setting, to discuss new techniques and to learn about new areas of research. I have incorporated some of the material from the summer school and workshops in teaching my Biomathematics course at my home institution and in advising my graduate students in their research. It was at the BIRS activities that I first met research professionals in my area including Jainhong Wu, Troy Day, Mercedes Pascual, Zhien Ma, David Earn, Ping Yan, among many others.

The accommodations, meals, and facilities at BIRS Center have been excellent. The BIRS center, located in a beautiful setting in Banff, is an ideal place to concentrate on research without distractions from professional or personal responsibilities at your home institution.

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Uri Abraham, Professor, Departments of Mathematics and Computer Science, Ben-Gurion University

I have participated in two conferences in Banff, one in mathematics (in the area of set theory) and another in computer science (on self stabilization), In both workshops the participants included the world leaders in these fields, together with working scientists from many different countries, young researchers, and PhD students. I think that these workshops contribute not only to the advancement of science at the highest level but also to the sense of international unity in science and to the place of Canada as a promoter of this movement.

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Stephen Wilson, FIMA, Professor, Head of Mathematics, University of Strathclyde

I attended the BIRS workshop on "Nonlinear Dynamics of Thin Films and Fluid Interfaces" and found it a very stimulating and intellectually satisfying. The participants were a hand picked and very high powered team of international experts and as a result the meeting was of a very high class. The unique environment helped to create an environment very condusive to academic collaboration and the local facilities and arrangements were uniformly excellent.

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Mourad Ismail, Professor, Department of Mathematics, University of Central Florida

I was invited to BIRS twice with the most recent in the Fall of 2008. I greatly enjoyed the atmosphere, the lectures, and, of course, the scenic view. I am a university of Alberta Ph D so I have been to Banff many times but BIRS is a real gem.

The format of the conference was very beneficial to me. I am in orthogonal polynomials and special functions and the conference was on spectral analysis and asymptotics which overlaps with my own research interests. I had some ideas for research problems from listening to the talks and the presence of many first rate people was a golden opportunity to exchange ideas and get information.

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Susan Montgomery, Professor of Mathematics, University of Southern California

The two meetings I have been to recently were excellent:

1. March 2008, on algebraic topology and Hopf Galois theory. This was really interesting to me, to see that Hopf Galois theory had applications in topology. I wrote one paper from the algebraic point of view for the proceedings of this meeting. But for me the most important part was to broaden my horizons, both in terms of new directions and in terms of meeting new people.

2. October 2008, non-commutative algebra and algebraic geometry. This topic is closer to the area in which I was trained, though I had gotten away from it. But it was very interesting to see new developments, and now I have a Ph D student working on some related problems.

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Krzysztof Burdzy, Professor, Department of Mathematics, Department of Statistics, University of Washington

The Banff International Research Station is a wonderful conference center. I participated in 2 or 3 conferences there and I found them as rewarding as any other conference.

Not every conference results in a tangible benefit to my research. But I can trace one particular case to a BIRS conference (in addition to non-tangible but significant benefits). Balint Virag, a brilliant junior mathematician, bast at the Univ of Toronto, heard me present a conjecture based on computer (numerical) calculations. He supplied a rigorous proof and I was able to include it (with proper attribution) into one of my papers.

I hope very much that BIRS will continue its activities.

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James L. (Jay) McClelland, Professor, Department of Psychology, Director, Center for Mind, Brain and Computation, Stanford University

The workshop I participated in on probabilitistic approaches to development was outstanding. It brought together a larger group than usual for a small workshop and included most of the important figures in the field and certainly representatives of all relevant points of view. The facilities including a/v computer and logistical support were outstanding. In my case the event afforded the opportunity to understand in detail a perspective that has been of growing importance in my field, and to have the chance to have first hand conversations with most of the key researchers in this new `tradition'. A pair of back-to-back papers will appear in Trends in Cognitive Science as a part of an ongoing dialog with this group that was continued and extended at this meeting.

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Doron Lubinsky, Professor, Department of Mathematics, Georgia Institute of Technology

It is a privilege to provide some perspectives on the impact of the Banff conferences. I'll report here on one of them, ``Modern Approaches in Asymptotics of Polynomials", Sunday, November 11 to Friday, November 16, 2007, organized by Peter Borwein (Simon Fraser University), Doron Lubinsky (Georgia Institute of Technology), Ed Saff (Vanderbilt University).

There was a lot of interaction between several groups with different approaches to asymptotic of polynomials, especially orthogonal polynomials. These include the Riemann-Hilbert approach of Deift-Zhou et al, the operator approach of Simon et al, and older approaches involving potential theory, and classical methods.

Several papers grew out of this: in my own case, the idea of using de Branges spaces to describe universality limits arose out of this conference. It led to the paper ``Universality Limits for Random Matrices and de Branges Spaces of Entire Functions", Journal of Functional Analysis, 256(2009), 3688-3729.

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Alex Figotin, Professor, Department of Mathematics, University of California

The BIRS is an excellently organized and very efficient research center. I was there two times, last time in April 2009. Both times BIRS provided very good environment to discuss issues of interest with my peers. Some of these discussions initiated collaborations which may result in joint research papers. BIRS has a wonderful location providing nice opportunities for active relaxation such as hiking and spectacular nature viewing. I hope in the future to come back BIRS.

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Michael Harris , Professor, Department of Mathematics, Université Paris-Diderot

I am pleased to share my experiences as primary organizer of two back-to-back research programs at the Banff International Research Station (BIRS) in the summer of 2008. I have organized a number of international meetings and research programs, and I believe that the programs at Banff were particularly elaborate and challenging because of the scope of the material involved. The first week was a summer school for graduate students and non-specialist senior mathematicians, the second a research conference, both centered on the contents of the Paris project to publish a series of books on the stable trace formula and its applications to number theory, and on Arthur's forthcoming book on automorphic forms on classical groups.

As primary organizer, it would be inappropriate for me to praise too effusively the contents of the meetings. There is no doubt in my mind, however, that the organization of these meetings was crucial in bringing the book project into existence. Most of the book's chapters were represented by lectures at BIRS. The first book of the Paris series is now effectively complete, including the final chapters containing original results by Clozel, Labesse, and myself. The table of contents of the second book is completely mapped out, in large part thanks to preparations for the BIRS programs. Thus I can say that the BIRS helped considerably to create what I hope will be a valuable resource for students in the field and colleagues in related branches of number theory; it also helped create the conditions for the successful completion of my collaboration with Clozel and Labesse.

Space is limited at BIRS, and a number of colleagues and students had to be turned away, especially from the first week's program. Others were unable to attend because of schedule conflicts. This circumstance had an unexpected benefit: there was sufficient interest in being able to view the lectures on line that funds were found to finance the filming and streaming of all lectures of both week's programs. The resulting series of videos is a uniquely valuable introduction to the techniques and use of the stable trace formula; I have already used this resource successfully with my graduate students. The organizers made a special point of providing ample time to Jim Arthur to present the contents of his long-awaited book. I believe the films of his lectures are the first and, for the time being, still the only source for complete statements of his fundamental results.

It remains to add that the BIRS staff was superb and the organization was flawless. I may not have the energy to organize another meeting at BIRS (or elsewhere) but I would definitely be grateful for the opportunity to return to BIRS in the future as a simple participant.

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Keshav Dasgupta, Assistant Professor, Department of Physics, McGill University

I have been visiting Banff for the last four years. My first visit was in the summer of 2006, where we had an intensive group interactions with Cliff Burgess (from PI), Jim Cline (from McGill) and Hassan Firouzjahi (also from McGill). This collaboration led to the paper: ``Uplifting and Inflation with D3 Branes" (archive number: hep-th/0610320), the results of which have been used by many colleagues in our field. I would say that this paper wouldn't have been written if we were not at Banff. Banff provided us with an ideal atmosphere where we could do our research uninterrupted and with minimal distractions.

My subsequent visits also led me to work on other papers and projects with least amount of distractions. For example the ideal research atmosphere in Banff led us to work on another paper titled: ``Lumps in the throat" (archive number hep-th/0702193).

I have also visited Banff for shorter visits to present some results of my research in a string conference held in the winter of 2009. The interactions at Banff, and the subsequent feedbacks that I got on my talk were very useful in improving the contents of my paper.

For all the above reasons, and many more, I would say that my visits at Banff had been very useful in my research. I would be very happy to visit Banff regularly in the coming years.

Last but not the least, the accommodation and food at Banff were excellent. Also the staffs and the officers at Banff were always very helpful (especially Brenda Williams). I could safely say that right now the academic atmosphere in Banff is unparalleled.

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Patrick Hayden, Associate Professor, School of Computer Science, McGill University

Participation in the BIRS workshop Operator Structures in Quantum Information was absolutely inspirational. It brought together two communities, one, quantum information, full of problems and eager for new techniques with the other, operator spaces, possessing a finely-honed collection of tools delighted to find a new domain of application. Discussions at the workshop reintroduced me to a longstanding conjecture in quantum information known as the maximal p-norm multiplicativity conjecture. About 6 months later, I managed to disprove the conjecture for all important values of ``p", setting the stage for Matt Hastings' disproof the following year of the ``additivity conjecture" of quantum information, universally acknowledged as the most famous conjecture in the field. The facilities at BIRS were excellent, the atmosphere congenial and the company brilliant. BIRS has rapidly taken its place among the most influential mathematical research centers in the world.

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Osmo Pekonen, University of Jyväskylä

I am a science journalist writing in English for an international magazine but I am based in Finland which is a small country. I participated in an event at Banff which allowed me to have important exchanges with colleagues from other media and other language areas. The experience was extremely valuable and highly rewarding for me. I am looking forward to returning to Banff next year. The working environment was stimulating and of a scenic beauty. This made my stay unforgetable; it was also the only time that I have visited Canada. At home, I published a travel story about my experience.

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Oscar P. Bruno, Professor, Department of Applied and Computational Mathematics, California Institute of Technology

I participated in a meeting at BIRS in the last four years. That was an excellent experience, in that it allowed me to lend exposure of my work to a wide international audience, as well as to learn from a wide range of researchers, some of whom I had not had an occassion to meet previously. My stay at BIRS was a most stimulating one - I certainly hope such opportunities will continue to be available to the mathematics research community in years to come.

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Paul Hildebrandt, Executive, Co-Founder, Zometool

Although I'm not a scientist nor mathematician, I did experience what could be a significant advance in my field of mathematics while attending the Renaissance Banff Bridges 2005 conference. My company manufactures and markets Zometool, which can be thought of as a kind of canvas for the art of mathematics. During the conference, some attendees organized the impromptu construction of 2 members of the H4 group, which, to our knowledge, had never before been modeled in 3 dimensions. Concurrently, several of my associates Dr.s David Richter and Scott Vorthmann, and the late Jean-Christophe Kling - discussed the math underlying Zometool and arrived at the theory that is a physical manifestation of E8. Dr. Robert Moody seemed to concur. E8 has recently gained notoriety as the basis of A. Garrett Lisi's ``Exceptionally Simple Theory of Everything."

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Paul Tseng, Researcher, Department of Mathematics, University of Washington

I participated in a Nov 2006 BIRS workshop, and it was very useful for research discussions with ``old" and ``new" colleagues in my area of research, optimization. The workshop had a good mix of senior people and recent PhDs, and it was particularly helpful to meet the young researchers. In fact, one of them applied to a tenure-track position in our department that year and we made an offer.

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Cenk Sahinalp, Professor and Canada Research Chair, School of Computing Science, Simon Fraser University

This letter is for expressing my enthusiastic support for BIRS and its programs especially at the interface of mathematics and theoretical computer science. The workshop I co-organized on the mathematics of string spaces and its algorithmic applications was the first of its kind and brought together world experts on combinatorial pattern matching, approximation algorithms and metric embeddings. For the first time since exploration of string spaces started such a wealth of expertise came together for a common goal. Understanding of string spaces - which are generalizations of discrete vector spaces - is essential to many applications in computational genomics, natural language processing and the web. The effort initialized by this BIRS workshop will help lay the foundations of ``string space exploration".

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Craig Tracy, Distinguished Professor, Department of Mathematics, UC Davis University of California

I attended the workshop "Recent advances in algebraic and enumerative combinatorics" (May 3-May 8) It was my first (and only) visit to BIRS. The workshop was helpful to me at that point in my research since the connections between combinatorics and random matrix theory were being actively explored by the research community. I benefited in meeting a number of the leaders in combinatorics.

Viewed from afar BIRS seems to be quite successful in promoting research and bringing together different fields.

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Dominique Arlettaz, Rector of the University of Lausanne

I attended once a conference at the BIRS and I enjoyed it very much. The place is wonderful and provides an extremely quite athmosphere, which is essential for doing good mathematics. I can only say that a stay at the BIRS is great in order to create new contacts and to get new ideas.

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Radu Cebanu, Graduate Student, Universite de Quebec a Montreal

I am a second year graduate student and I participated in the workshop ``Interactions of Geometry and Topology in dimensions 3 and 4" held at BIRS in march. It was a very useful experience for me because I learned very much from the talks which had a wide coverage and also from unofficial conversations (which wouldn't have been possible otherwise). I learned about the current developments in the field and I also found an interesting and challenging project for my PhD from one of the talks.

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Lou Ann Gerken, Director, Cognitive Science Program and Tweety Language Development Lab, Professor, Department of Psychology, University of Arizona

I recently attended the Banff Probabilistic Models of Cognitive Development (May 25-29, 2009). The workshop was extremely helpful to me in developing a research proposal to the NSF to pursue some of the questions that were raised during formal and informal discussions. My proposal is infinitely more informed about new, unpublished research in my field than it would be if I hadn't attended the meeting. The setting, in which my group ate, hiked, and of course presented, was ideal for letting us explore in depth questions that will set the research agenda for the next several years.

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Ed Green, Professor, Department of Mathematics, Virginia Polytechnic Institute and State University

My participation at the BIRS workshops have been very useful mathematically and also very well run and enjoyable.

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Pavel Bochev, Distinguished Member of the Technical Staff, Applied Mathematics and Applications, Sandia National Laboratories

I had the opportunity to visit BIRS in April of 2009. I was invited to take part and speak at the workshop on “Advances and perspectives on numerical methods for saddle-point systems” organized by H. Elman (U. Maryland), C. Grief (UBC), D. Schoetzau (UBC) and A. Wathen (Oxford). My primary research area is finite element methods for partial differential equations which are an important source of saddle-point problems. The workshop provided me with an excellent opportunity to get up to speed with the most recent algorithmic and theoretical advances and talk to some of the top experts in this field. One of the best aspects of BIRS workshops is the opportunity for informal meetings and discussions with the colleagues. I had many of these and they were as useful and informative as the regular sessions, in particular, discussions that I had with professors Szyld and Haber. Besides clarifying some subtle points of their research these discussions shed important light on some of my own research projects While nowadays we have almost instantaneous access to abundant scientific information, nothing compares to a live, immediate interaction with someone who has deep and thorough understanding of a research area and can provide an insight rather than just raw information. This is perhaps one of the most valuable aspects of BIRS which renders a tremendous service to the mathematical community.

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Robert Buckingham, C.R.M., Department of Mathematics Universite de Montreal

I participated in the BIRS workshop on Random Matrices, Inverse Spectral Methods and Asymptotics in October 2008. This was the most useful conference I have attended in the past year. The size is perfect for a serious research conference. Enough people that there are many new and interesting talks but few enough that it remains focused. The meeting was very beneficial to my research, as well. I was able to meet with two colleagues, one from Montreal and one from Texas, and get a significant start on a project we had been discussing over email. We are now finalizing the paper for submission.

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Faisal Beg, Associate Professor, School of Engineering Science, Simon Fraser University

I was fortunate to be invited to one of these gatherings. The experience was memorable. I got a chance to have long discussions, over breakfast, over lunch, over dinner, around a fireplace, during the talks - and it made a significant difference in the direction of research that I have undertaken in the time since then.

Several journal papers (at least 4) have come out of my work that have surely been influenced by the discussions and the presentations I participated in at BIRS.

I sincerely hope that BIRS will not only continue, but grow. It is an extremely innovative and effective way to bring together scientists, and thereby facilitate good science.

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Scott Sheffield, Professor, Department of Mathematics, Massachusetts Institute of Technology

I have found my Banff experiences extremely productive and useful. Twenty to thirty participants in a very pleasant and somewhat isolated facility with beautiful natural surroundings - with plenty of space to talk and all events close to one another - it is really the perfect setting for mathematical research. Both the science and the logistical administration were always superb.

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Mihai Putinar, Professor, Department of Mathematics, University of California at Santa Barbara

I am happy to comment my past activities at BIRS: three workshops and one focused research group, among which I was the co-organizer for two of them. All during the last three academic years.

Each time I arrived at the beautiful Banff Center with a long list of expected things to accomplish, and I left with much more: with the precious and non quantifiable twist of the surprise and revelation element, so specific to the genuine research activity. The unique atmosphere of the center was every time a catalyst of intense, constructive discussions, new collaborations and a clearer picture of the future investigations.

Just to give a few examples: during the 2006 workshop on Positive Polynomials I have started a collaboration with Jean Bernard Lasserre and John William Helton which led to a publication hosted by Annals of Probability. The workshop devoted to Laplacian Growth I coordinated in 2007 led to an ample survey and completely original article, joint work with Mark Mineev and Razvan Teodorescu (both of Los Alamos Laboratory), just published by the Journal of Physics: A. The focused research activity of 2008 devoted to the Geometry of Polynomials has opened a vast array of intriguing questions about the rather old and non-answered Sendov-Iliev conjecture. Sadly, one of the members of the team, Dr. Julius Borcea of Stockholm University, has died a couple of months ago in tragic circumstances. The members of the team are continuing now this exciting path of work, most likely leading to the publication of a monograph aimed at preserving his memory.

I can surely state that my recent research calendar was profoundly enhanced by the activities I have been part of at BIRS. And will continue to be, as I plan to attend three workshops in the near future. Every time I left BIRS I had the deep impression that I am now member of a new family of researchers, all sharing a novel, uncharted territory of research.

On the logistics side I must also praise BIRS for the simplicity of the application procedure and the efficient help offered to the organizers of workshops. The excellent accommodation conditions, the informal and flexible structure of the working days and the serenity of the surrounding mountains are also notable.

On all grounds BIRS is today the American counterpart of the Mathematical Research Institute at Oberwolfach (Germany).

Thank you for your efforts of raising and maintaining BIRS at the high level it has achieved in 2009.

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Feng Rong, Researcher, Syracuse University

I visited BIRS this March. As a young researcher (postdoc), I of course cherish every opportunity to meet with senior mathematicians and get some update on the field. And the week I spent at Banff was very productive. I talked to many people and had some ideas about certain problems. I have been able to finish writing a paper in the past few months. Moreover, on a more personal note, this meeting in Banff was very refreshing since I was then on the job market and was quite stressed out. After traveling to Banff, I could put the job hunting behind me for a week and just focus on mathematics while having some quality time with my colleagues.

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Felipe Voloch, Professor, Department of Mathematics, University of Texas

I attended a conference at BIRS in 2005 and was very enjoyable. I very much liked the ``Oberwolfach" style of the conference. It had a similar spirit and a similar crowd to other conferences I attend from time to time but I was glad this one was in North America and not in Europe for a change.

Thank you for running such a nice conference center.

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Jingyi Chen, Professor, Department of Mathematics, University of British Columbia

I have had wonderful experience at BIRS. The workshop on Minimal Submanifolds and Related Topics attracted a lot of world-leading experts in the field as well as quite a few very talented young researchers. I found some of the results reported in the workshop are very interesting, open problems and new research directions discussed there are very useful and informative. I also met several experts whose work are well known to me but I didn't meet them before.

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Lei Ni, Professor, Department, of Mathematics, University of California, San Diego

Banff center is very important for mathematics especially in terms of providing the opportunities for mathematicians from different branch to interact. I personally benefited from such interactions. It is absolutely essential to the development of the young mathematicians in their early career.

I also like a lot the idea of the focused research groups (in pairs) so that people can spend time with their co-authors to finish up a project.

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Shihoko Ishii, Professor, Algebraic Geometry, Singularities, Tokyo Institute of Technology

Thank you for your message. I visited BIRS twice. Both times the activities were wonderful. The talks were exciting and the discussions were very stimulating. Based on the questions asked after my talk, new problems have been posed. I am now working on these problems.

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Bruno Courcelle, Professor, Department of Computer Science, Institut Universitaire de France

I have participated to one seminar (Graph Minors) at Banff, in September 2008.

The organization was excellent on all respects: - The seminar was announced several months in advance, permitting participants to arrange travels conveniently, - Location, rooms, food, local facilities (computer in room, printing close to the room) are excellent, - Information about airport shuttles etc... is excellent.

The seminar gathered many experts of the field. I could work with other participants (S Kreutzer, I. Adler from UK and Germany), and we are planning to write an article together. That we could meet for several days was important for this work.

I am looking forward to attend other meetings there, although it is a bit far from my place (Bordeaux, France).

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David J. Hand, Professor, Department of Statistics, Imperial College, London, President, Royal Statistical Society

I have participated in one meeting (on measurement theory and methods) at the BIRS, and co-organised another (on credit risk). Both of these meetings were extremely stimulating and very successful.

The first allowed me to establish new links with researchers working in the area of my paper [Hand D.J. (1996) Statistics and the theory of measurement (with discussion). Journal of the Royal Statistical Society, Series A, 159, 445-492.] and materially aided me in developing my book [Hand D.J. (2004) Measurement theory and practice: the world through quantification, Edward Arnold.].

The second allowed interactions between many of the world’s leading researchers in retail credit scoring. One consequence of this was the fact that a consortium of three of us successfully won a UK Engineering and Physical Sciences Research Council competition to establish a Centre focusing on this topic. The initial funding for this Quantitative Financial Risk Management Centre has now finished, but the Centre itself is continuing. Many PhD students have successfully graduated from this Centre, and others are in the pipeline. Likewise, several postdocs have been supported.

The particular strength of the ‘Banff experience’ is that the relatively small size and intimate nature of the meetings permits very useful scientific interactions between the workshop participants.

It is very clear that the BIRS provides an ideal working environment for stimulating intellectual advance.

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Bo'az Klartag, Associate Professor, School of Mathematical Sciences, Tel-Aviv University

I participated at the ``geometric inequalities" workshop in Banff, 2004. It was not a large conference, with 30-40 carefully chosen participants, the world leading mathematicians of the field. It was a delightful experience. I just finished my PhD, and I remember that I learned a lot from the lectures and also from side discussions with other mathematicians. The environment is perfect for mathematical research.

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Omri Sarig, Associate Professor, Department of Mathematics, Pennsylvania State University

I have participated in the meeting ``Rigidity, Dynamics, and Group Actions" organized by Dave Morris, David Fisher and others at Banff in the summer of 2005. The meeting was one of the most effective ones I have ever attended. The very best people in the area have attended, including the Fields medalist Margulis (the Fields medal is the highest prize in mathematics), as did many post-docs and beginning mathematicians. There were many research activities beyond the usual ones in ordinary conferences: small group discussions, discussions during long walks etc. I have no doubt that the beautiful location and superb facilities offered by the Banff research station had a role in attracting such an excellent and diverse group of people.

There is a European research center similar to the Banff research center in Oberwolfach , Germany. Some of the very best maths conferences take place there. In my opinion the Banff research center is even better than Oberwolfach. It is without any doubt the best resort for maths conference I have ever attended, certainly the best in North America.

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Yihong Du, Professor ,School of Science and Technology, Mathematics Section, University of New England

It is my pleasure to testify that the Banff workshop I attended in Oct. 2007 was very valuable for my research. I was able to exchange information about research progress with many other participants at the workshop in an environment which stimulates new ideas. In particular, I was able to discuss with Prof. H. Matano (Univ. of Tokyo) about further research on our joint work, which led to a positive answer to a question posed by Prof. H. Brezis.

I very much hope that BIRS can continue to hold such workshops in the future.

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Jerome Droniou, Professor, Department of Mathematics, Universite Montpellier

I attended the workshop``Non-local operators and applications" organised at the BIRS in April 27-May 2, 2008. It was not only a very pleasant professional experience, but also a fruitful one, since the discussions I had allowed me to strongly improve a work I was doing at the time on numerical methods for fractal PDE (opening some interesting lead to have an efficient scheme even in dimension 2 or 3). It also allowed me to take new contacts with people I had never met before, but whose works I was familiar with.

The facilities and service you provide to researchers are really appreciable and of high quality.

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Roger Wets, Department of mathematics, UC Davis, University of California

During the last 4 years, I participated in a number of conferences, of different character, at BIRS. For me these events have been extremely rewarding since they have led me to enter a couple of new areas, or at least make the tie to research areas that had not been part of my research-horizon before those BIRS-meetings. In addition the in-depth presentations at some of these meetings have given me a deeper appreciation and understanding of certain areas: of the problems that need to be dealt with, of the value of alternative tools used in those areas. I have always been able to stay the full five days, even once longer, and that has been particularly fruitful since it has made possible the non-trivial interaction with the other participants; the easy availability of colleagues is essential to foster such contacts.

I would encourage the program committee to accept proposals for a combination course/research lectures (over a 2 weeks period). By courses, I would mean a few extended presentations by some leaders in the field, complemented by a more standard series of lecturers by other participants.

BIRS is the best thing that happened in North America in support of the Mathematical Sciences!

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Kreso Josic, Associate Professor, Department of Mathematics, University of Houston

Attending the meeting at BIRS several years ago was a real pleasure. I can honestly say that it is among the top 2 or 3 meetings I have ever been to. I had just stated as an assistant professor at the University of Houston at the time, and BIRS offered a great setting to meet potential collaborators and discuss new ideas.

In particular, this is when I first started collaborating with Brent Doiron - an ongoing collaboration that has resulted in several publications, including one in Nature. In fact, Brent and I are co-organizing another workshop in Banff in 2010, and are certain that it will be equally successful.

I believe that the work of the center is of fundamental importance, and sincerely hope that it will continue in the future.

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Etienne Blanchard, Researcher, Institut de Mathematiques de Jussieu

I really enjoyed coming to the BIRS in November 04 for a workshop on The structure of amenable systems. I started there working with Simon Wassermann on exactness problems. This ended with the publication of the paper Exact C7-bundles, Houston J. Math. 33 (2007), 1147-1159.

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Tyler Jarvis, Chair, Department of Mathematics, Brigham Young University

I really appreciate the opportunities I have had to attend workshops and conferences at BIRS. All of them have been beneficial to me, but the most recent one I attended (May 2008), resulted in a new collaboration with Professor Dan Edidin.

As a result of that collaboration, Takashi Kimura, Dan Edidin and I have been able to explicitly describe the multiplication in orbifold K-theory for orbifolds which are not quotients by finite groups. This is a problem that has been of interest for quite some time and I think BIRS deserves much of the credit. The results are described in the paper ``Logarithmic trace and orbifold products" (arxiv.org/abs/0904.4648)

We have several more results in progress right now and expect those to be written up soon. It is unlikely that any of this work would have happened without our having met at BIRS last year.

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Ortrud Oellermann, Professor, Department of Mathematics and Statistics, University of Winnipeg

I have helped to organize two focused research group workshops at BIRS (one in 2006 and one in 2008). Both workshops were very successful and have resulted in three research articles. Having had the time to interact in small groups was very beneficial. Most of the ideas for these research papers were developed during our time at BIRS. I hope that BIRS will be able to continue offering such opportunities to the mathematical research community.

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Johannes Kellendonk, Professor, Department of Mathematics, Institut Camille Jordan

It is a pleasure for me to tell you how much I appreciated the two meetings I had at the Banff center since it has opened. The first one was a two-weeks focused research group, which I organised in 2005 together with Ian Putnam and Jean Bellissard, and the second was a 20 participants workshop in Octobre 2008. Both meetings had a lucky composition of participants who had an extremely open minded spirit with everyone willing to share knowledge. The wonderful atmosphere at Banff with its marvelous infrastructure attributed to this so that these two meeting stand out as some of the best I have ever been to. As in science brainstorm induced creativity plays such an important role the above-mentionned qualities matter very much. I heard from the participants of the focused research group (the October 2008 meeting being still a bit recent) that lot's of papers were kicked off by ideas developed during that event. I sincerely hope that the good start is going to be continued.

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Ryan Hayward, Professor, Department of Computing Science, University of Alberta

Banff is a world-class destination resort, and the acceptance rate of international scholars who are invited to BIRS workshops is very high. Each BIRS workshop I have attended has given me daily face-to-face access to world experts; this to me is the benefit of the BIRS program.

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Norman Levenberg, Professor, Department of Mathematics, Indiana University , Affiliation

I am writing to express my gratitude to BIRS for the opportunity to attend the Complex Analysis and Complex Geometry session recently (May 31 - June 5). I have been fortunate enough to have participated in several BIRS workshops in the past few years. The first one, in pluripotential theory several years ago, was excellent, yet each successive meeting was more and more worthwhile. During the Complex Analysis and Complex Geometry session, I had the good fortune to meet a brilliant young mathematician, Sebastien Boucksom, with whom previously I had only e-mail contact. Sebastien`s talk, along with that of his collaborator, Vincent Guedj, unlocked a new (variational) approach to the highly non-linear complex Monge-Ampere operator which should open doors to future progress in pluripotential theory. Even more helpful was a several hour blackboard session with Sebastien and one of my collaborators, Len Bos, in which Sebastien elaborated on this variational approach and explained his previous deep work with Robert Berman. Overall, the combination of interesting talks together with a relatively small group of researchers with common interests in a highly stimulating setting has made BIRS an extremely desirable destination for me and other fortunate mathematicians. Once again, I thank you and the entire BIRS organization for your efforts.

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Steven L. Tomsovic, Professor and Chair, Department of Physics, Washington State University

I participated in one event at BIRS in February, 2008, I believe. The program was excellent. The organizers took their work seriously and made everything run very smoothly. In terms of administration, comfort, etc... it was great. I would especially like to thank Rob Whitney (whom I met for the first time at BIRS).

Scientifically, it was also excellent. A community of mathematicians got together with a group of theoretical physicists or mathematically inclined physicists. This is the only event that I am aware of in which these 2 particular communities got together. There were clearly different perspectives and vocabulary, etc... between the groups. It would be silly to say that all that was broken down in a week or so, but it was an important start. Within communities, the best people were there and the discussions valuable. I am personally continuing a collaboration with a couple of the participants, and it was valuable to me for that opportunity.

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Jonathan Goodman, Chair, committee on Mathematics in Finance, Courant Institute of Mathematical Sciences, Professor, Department of Mathematics, New York University

I went to a BIRS workshop on computational relativity. The workshop was small and did not have some of the major players in the area. As it turned out, it had the best players, however. At the conference one of the participants announced results that since have transformed the field. It was very helpful for me personally to talk freely with the physicists, as I was not an expert on relativity.

I have to say, it was one of the most productive workshops I've ever been to. I haven't gone on to work in that area myself, but the general background has affected my work considerably.

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Adam Siepel, Assistant Professor, Department of Biological Statistics and Computational Biology Cornell University

I participated in a workshop on computational and statistical genomics at BIRS in the summer of 2006 and I was extremely impressed with the facilities, the setting, and the BIRS staff and organization. We had a small and informal but highly productive workshop with an interdisciplinary group of attendees (statisticians and molecular biologists). The BIRS setting was ideal for getting to know one another and breaking down disciplinary boundaries. It was especially nice to be able to stay together on the Banff Center campus, and to be able to escape into the wilderness for an occasional hike. I have continued to keep in touch with other attendees of the meeting. Since attending, I have enthusiastically recommended workshops at BIRS to many of my colleagues.

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Robert Woodrow, Deputy Provost and Associate Vice-President (Academic), University of Calgary

I have been fortunate to take part in two workshops recently, and was invited but unable to take part in some others, which is a loss.

The first workshop was a full-scale event, Infinite Graphs, October 14-19, 2007. This brought together experts from several countries and featured a series of talks on cutting edge research of the participants. The meeting provided me with an update on areas that I've long been interested in, and also more work, in the form of writing referee reports about articles submitted for the proceedings of the meeting. From my discussions with others attending, I know that the opportunity to work together resulted in some strong progress on existing problems, on the formation of new collaborations, and the exchange of key information.

The second meeting was much more recent. It was a small working group on Indecomposable Binary Structures, June 15-21, 2009. This meeting brought together eight experts in the area and featured the work of the participants. It allowed us to become familiar with the latest efforts of colleagues whose interests overlap. I know that at least one article will flow from the discussions that were had. I have argued since the idea of BIRS was first proposed that North America needs just the sort of opportunity that BIRS presents. Mathematics and its applications benefit more than most from bringing together experts in the area and setting them in a situation that encourages free discussion and creative collaboration. Sometimes problems are resolved during the time of a workshop. More frequently, seeds for advances are sown and future collaborations are launched that result in results that go well beyond the period that is spent in Banff working closely together. In my view BIRS is an ideal situation, and we are extremely fortunate to have the success that it has brought.

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Aaron Brill, Research Professor, School of Radiology and Radiological Sciences, Vanderbilt University Medical Center

I attended a meeting organized by Anna Celler a few years ago dealing with dynamic medical imaging. The meeting was very successful. It brought together people from Canada and the United States working at the forefront of the field. Much of the work dealt with imaging of dynamic processes in the body, noninvasively. I think we all learned a great dealt about new approaches, and new technologies. Mathematical and computing resources that are at the leading edge in Canada were brought to our attention in the course of the meetings. I think collaborations emerged from the meeting that would not have come about otherwise. I know of several grant-supported projects that emerged involving participant in the workshop. I continue to pursue options with Anna Celler with respect to Compton Coincidence imaging an area that we pursue independently, but which hopefully will further develop with time. In any case the meetings are very important, and the site well suited to such state of the art conferences. I am particularly interested in coupling pharmacokinetic parameters describing biological turnover of new drugs for cancer therapy, and other problems areas. One can model turnover based on extensive data obtained in early phase drug testing albeit in restricted numbers of patients. Lesser kinetic information is obtained in Phase 4 when the drug is used in larger populations. It is in this latter case that one has the opportunity to establish patient specific parameters that include toxicity and outcome measures that lead to guidelines for best practice uses. In this case there is more sparse quantitative data for modeling. This is not my field of expertise, but it is an area in which mathematical models will play an important role. Patient specific data (including molecular genetics), and disease specific (including tumor) markers will be important parts of the modeling system. I believe the interconnected computer grids and mathematical expertise presented at the meeting, and under continued development by experts in your community will make important contributions in these areas, and I hope that this is one of the areas they may consider exploring. I encourage further biomedical conferences pushing the role of mathematics in medical applications.

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Urs Frauenfelder, Professor, Department of Mathematics, Ludwig Maximillians Universitat Munchen

During my stay at Banff an important cornerstone for the development of Rabinowitz Floer homology was laid.

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Kris Vasudevan, Researcher, Department of Geology and Geophysics, University of Calgary

I attended two BIRS workshops, one organized by Dr. Gary Margrave on ``Time-frequency Analysis". and one by Dr. Elena Braverman on ``Wavelet Transform Methods". I benefited a fair amount from attending these two workshops. Also, it allowed me to establish links with foreign scientists. Although the attendance has not been translated into joint publications with either one of the above-mentioned authors, the experience I have gained from these workshops is helping my present work.

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Jason Morton, Postdoctoral Fellow, Researcher, Geometry of Statistical Models and Algorithms, Stanford University

I participated in the Banff Workshop: Data Analysis using Computational Topology and Geometric Statistics, Sunday, March 8 - Friday, March 13, 2009. It was a very rewarding experience and enabled me to make several new connections as well as deepen existing collaborative relationships with researchers. The isolation and thoughtful combination of residences and friendly common spaces were tremendously useful in building community. I found that workshop attendees were more likely to spend time together talking late into the evening after hours than at other similar workshops I have attended at different locales. The international focus was in force at this workshop, as new ties were easily built between far-flung researchers, and the aforementioned conducive environment ensured that they went beyond quick acquaintance.

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Anne Schilling, Professor, Department of Mathematics, University of California

In 2007, Nicolas Thiery and I organized a 2-day workshop as a start-off meeting for the FRG NSF funded project ``Affine Schubert Calculus". The workshop focused on the computational part of the project, in particular MuPAD-Combinat. This has led to a long-standing collaboration both mathematically as well as computationally. In the meantime, we have switched to Sage-Combinat and implemented many features such as crystals, root systems, and symmetric functions.

In March 2008 I was part of a workshop which led to very fruitful interactions with Masato Okado where we made progress on the combinatorial model for Kirillov-Reshetikhin crystals for type $C_n^1$ and has led to the paper:

G. Fourier, M. Okado, A. Schilling, Kirillov-Reshetikhin crystals for nonexceptional types Advances in Mathematics, to appear ( arXiv:0810.5067 [math.RT] )

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Klaus Mueller, Associate Professor, Department of Computer Science, Stony Brook University (State University of New York)

I attended a BIRS seminar once. It was a great experience because of its free and informal setting, with only a tight circle of domain experts gathered around. There was ample time to critically discuss presentations with the speaker and also among the attendees. Lively and agenda-setting interchanges were the result, stimulating new research.

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Boaz Ilan, Assistant Professor, School of Natural Sciences, University of California, Merced

I would like to take this opportunity to commend BIRS for its excellent hospitality and efficient organization of scientific meetings. I participated in a weekend-long workshop in October 2008. The logistical and scientific organization was excellent and the relatively small-scale nature of the meeting allowed for a level of scientific and social interaction that exceeded my expectations. I believe that the charming location and the atmosphere in Banff play a key role in creating this open atmosphere.

The meeting I attended in 2008 allowed me to meet both senior and junior colleagues in my field. Most of those colleagues I had met the first time at that workshop. The interaction I had with them made a big impact on me in terms of exchange of ideas from the lectures and off-lecture discussions, collaborative work - I took the opportunity to do research with another participant (this work is culminating in joint paper), and getting to know program officers from funding agencies. For me, the BIRS meeting was very stimulating. Also, BIRS workshops do not charge the participants, which allows for less-funded (and typically younger) professionals to attend.

I am looking forward to participating in a five-day workshop in August 2009 and in future meetings.

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Rick Miranda, Interim Provost and Executive Vice President, Colorado State University

I attended a conference at the BIRS in the summer of 2007, in algebraic geometry. It was a most stimulating week, with wonderful accommodations, and a great variety of participants. Moreover from the very first moment I had interactions which have resulted in several new projects. I met Irene Swanson on the bus from Calgary, and we happened to sit next to each other; we had barely known each other before. While chatting, we discussed sandpile groups, something which was heretofore unknown to me. We had a lively conversation, and I soon realized that the entire concept had relationships with a paper one of my PhD students was reading at the time. Over the course of the week, Irene and I worked out most of the elementary theory ourselves, in several new ways, and when I returned to my campus I gave several lectures on sandpile groups to our geometry and algebra seminar. My student subsequently incorporated these ideas in an integral way into his thesis research, and he will graduate next year with a good project completed, in no small way assisted by what I learned at BIRS that week! This is a small example, but I am sure it is replicated many times throughout the year there at BIRS. The atmosphere of the institute is most conducive to collaborations and mathematical brainstorming, and I would urge the funding agencies to support the BIRS, and if possible expand it even, in the coming period.

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Heinz Bauschke, Full Professor and Canada Research Chair, University of British Columbia Okanagan

Question: What do you get when you put a group of motivated mathematicians together, feed them, expose them to stimulating talks, and give them enough time to brainstorm -- as it happens on a weekly basis at BIRS? Answer: Wonderful new theorems that would not have happened otherwise.

I was fortunate to attend the Canada-Chile math meeting, organized by Drs. Ivar Ekeland and Alejandro Jofre, in Fall 2005. The meeting had a clear optimization theme, it featured world-class speakers, and it left ample time for discussions. I have extremely fond memories especially of brainstorming sessions with Yves Lucet and Shawn Wang. At BIRS, we laid the foundation for a series of papers on the proximal average, a concept that allowed us to provide an answer to a question raised by Dr. Terry Rockafellar, the father of Convex Analysis, on the symmetric extension of a cylically monotone operator. The time at BIRS also led to a construction that allowed for the constructive (Zorn's Lemma free) maximal monotone extension of any given monotone operator. (In fact, I have been so impressed by BIRS that together with some colleagues we are co-organizing an interdisciplinary workshop in Fall 2009, with one of the goals being the recreation of this highly stimulating and productive atmosphere.) In summary, BIRS has had a crucial impact on my research career. And from discussions with colleagues, I know this is true for many other participants.

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Ari Stern, Postdoctoral Researcher, Department of Mathematics, University of California, San Diego

I participated in a BIRS workshop (07w5068 Geometric Mechanics: Continuous and discrete, finite and infinite dimensional) two years ago, while I was still a graduate student at Caltech, and it was a fantastic experience for me. This enabled me to interact with a wide-ranging group of international mathematicians, getting feedback on my own research (I presented some of my thesis work, which was then ongoing) and learning about other research areas that I might not otherwise have been exposed to. One of the most valuable experiences happened on a spontaneous hike that I took with the Portugese mathematician Rui Loja Fernandes and his student, Ivan Struchiner, where I ended up being introduced to me the concepts of Lie groupoids and Lie algebroids in Poisson and symplectic geometry. As a result, these tools have ended up playing a major role in my own research; this has also helped me to develop connections with the Iberian (particularly Spanish) mathematical community working in this area.

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Simon Guest, Reader, Structural Mechanics, Structures Group, Department of Engineering

I am very happy to write in support of BIRS. I have attended two workshops there, ‘Rigidity, Flexibility, and Motion: Theory, Computation and Applications to Biomolecules’ in 2008, and ‘Modeling Protein Flexibility and Motions’ in 2004. I found both workshops to be very effective means of developing new lines of academic work.

To give some particular examples:

(1) Following the 2004 workshop I started working with proteins for the first time, and my first PhD student in this area is now close to producing exciting results. Further, some of the work that I presented at the 2004 workshop on symmetry has been extended by the mathematical community: one paper now published on this is Connelly et al. (2009), and I know of other papers in preparation. I am also a co-investigator on a new application to the UK research councils on this topic with Bill Jackson, who I met at BIRS.

(2) Following the 2008 workshop I began working on zeolites for the first time, and this has led to a submitted paper, Kapko et al. (2009); this is but the first step in a very promising research programme.

None of the above work would have happened without the BIRS workshops: I am thus very grateful for the support to my work that BIRS has given; I hope to be invited to further workshops in the future; or indeed, may well apply to run workshops there myself. It would be a significant blow to the mathematics community, and those who collaborate with mathematicians, if BIRS were not to continue.

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Zbigniew Blocki, Institute of Mathematics, Jagiellonian University

I have participated in 3 workshops at BIRS (in 2003, 2004 and 2009) and I will soon come to Banff again, this time as an organizer. I have always enjoyed coming to Banff, both scientifically as well as touristically, but I understand you are mostly interested about the former :)

I believe that I have profited from participating in BIRS workshops a lot. The first one (``Monge-Ampere type equations and applications" from August 2003) allowed me to get in touch with many 1st class specialists in nonlinear PDEs (my main field being Several Complex Variables). With one of the organizers of that meeting - Pengfei Guan - I will soon coorganize (together with Duong Phong) a workshop titled ``Complex Monge-Ampere Equation", where many experts from Complex Geometry have promised to show up. My other two workshops were in the area of Pluripotential Theory and Several Complex Variables, and they were also very enriching to me.

Somehow, my impression always was that at BIRS workshops the most up-to-date state of research at a given field was being presented. I also like very much the format of the meetings, they were scientifically much more fruitful to me than bigger conferences. And I found the atmosphere in Banff Centre to be just perfect for research. I certainly hope this project will be able to continue in the future.

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Rafal Urbaniak, Postdoctoral Researcher, Centre for Logic and Philosophy of Science, Ghent University

The workshop I attended was one of the most prominent events related to logic taking place that year. It gathered many leading figures in my field, and discussions started at that workshop led to my cooperation with a leading British university on a new topic. As a result of a long chain of events that started in Banff, I will be spending the next semester in the UK as a British Academy Visiting Scholar.

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Fabien Durand, Head Researcher, Faculty of Mathematics and Computer Science, University of Picardie Jules Verne

I participated at a one-week conference at Banff on Aperiodic Order. I was very impressed by the very high quality of the accommodation and the natural site. Concerning the mathematics, it was the first time I was able to meet researchers from US working on tiling. The week was very stimulating and was the starting point for my interest in tiling. I have now several contributions in this topic. One of them clearly originated from Banff :

Self-similar tiling systems, topological factors and stretching factors, M. I. Cortez et F. Durand, Disc. and Comp. Geometry 40 (2008), 622-640.

and another is coming

Linearly repetitive Delone systems have a finite number of non-periodic Delone system factors, M. I. Cortez, F. Durand et S. Petite, accepted by Proceedings of the AMS.

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Andries E. Brouwer, Professor, Department of Mathematics, Eindhoven University of Technology

I participated once in a BIRS workshop, a few months ago. It was *very* useful. Because of the workshop I started research in a new area. (Or, perhaps more accurately, restarted work in an area that I had left long ago.) So far that has resulted in one submitted paper and more in preparation. Also, in useful contacts.

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Burt Totaro, Professor, Department of Pure Mathematics and Mathematical Sciences, Cambridge University

My comments on the Banff workshop on ``Applications of torsors to Galois cohomology and Lie theory", 23-28 April 2005:

The workshop was a chance for me to learn from the world's leading mathematicians in the areas of quadratic forms and linear algebraic groups. In particular, the subject of quadratic forms has been dominated in the past decade by the deeper methods of algebraic cycles introduced by Vishik and Karpenko. After I learned from both of them at Banff, I wrote a series of three papers on the birational geometry of quadrics, building upon their work. The meeting meant a lot for my research.

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Donald E. Marshall, Professor, Department of Mathematics, Department of Mathematics

I participated in a workshop on SLE in March 2005 at BIRS. The contacts made and the math problems encountered were instrumental in helping me return to the level of research I had attained before becoming chair at UW. My research is supported by the NSF again, which is unusual if not unique for a former chair from our department.

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Andrew R. Conn, Researcher, Mathematical Sciences, IBM T. J. Watson Research Center

This is only a brief testimonial and I usually do not have the time to respond conscientiously but I feel compelled to say something in this case.

The workshops at BIRS are outstanding. They are world class, certainly help to raise the perception of Canada in the international research community and are remarkable in their breadth. In fact I think they should be especially congratulated for inviting researchers in industry and in applications related to the interests of applied mathematicians but who are not themselves mathematicians. Everyone of my several visit have been memorable and have introduced me to important areas that I was not familiar with. Of course the location and the facilities also make it a delightful experience. Even in these times of stressed economies it would be extremely unfortunate for all of us and our fields if the funding for BIRS was reduced in any way.

In all honesty, the direct effect of my visits on my current research are difficult to quantify and my commitments at IBM have necessitated me to refuse more than one invitation in the past but every visit has the potential to have a major effect on my research and I would always attend for that reason alone if I am able to.

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Amelia Crowfoot Clark, Superintendent of Schools for the Siksika Nation

I found my involvement with the BIRS workshop very engaging especially as it relates to the indigenous ways of knowing. Having elders meeting with mathematicians was an exciting opportunity to participate in the exchange of western and indigenous knowledge.

As a First Nations mathematics educator, I have found the relationship between western science and indigenous knowledge very intriguing. Having hosted a science camp for youth since 1992 at a First Nations College, Old Sun Community College, we have incorporated Siksika knowledge with western science and have had amazing experiences.

Thank you for allowing me to participate in the workshop I attended a couple of years ago.

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Torsten Moller, Associate Professor, Department of Computing Science, Simon Fraser University

I had the privilege to participate in a number of workshops at BIRS and even co-organized one in 2004. Each and every time it is a pleasure to attend since BIRS is one of the only places where one has the chance to deeply discuss scientific problems without being in a hurry (like one is at a conference). This enables one to really brainstorm about the future of one's discipline. Another great experience of BIRS is the interdisciplinary nature of the meetings. It is truly unique to get to converse with the best minds of areas outside my own expertise. I have not experienced such deep exchange at any conference I have attended. It truly leads one to think outside the box and to excel. For example, our 2004 BIRS meeting resulted in a Springer book, that was just published this month (June 2009).

Last but not least, the staff at BIRS make it the most wonderful experience one can have. Bravo to them! (The wonderful surroundings and the setting of BIRS do not hurt either!)

I cannot even begin to imagine the loss to science if BIRS would cease to exist! Please don't let this happen!

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Jonathan Brundan, Professor, Department of Mathematics, University of Oregon.

I attended the meeting on ``Algebraic Lie Theory," May 27 - June 1 2007. During this time I initiated a collaboration with Catharina Stroppel (Bonn), which has since developed into a series of four articles on ``Highest weight categories arising from Khovanov's diagram algebra". The first three of these articles are posted on the arxiv, and the fourth is about to be posted. Along with other institutions such as Oberwolfach (to which I seldom travel due to its distance from the western United States) and MSRI, the research environment provided by BIRS is critical for stimulating interaction such as this one between researchers around the globe. My former graduate student, Jonathan Brown, also attended this meeting and was given the opportunity to give a 20-minute talk, the first experience in his career of lecturing to an international audience. He currently holds a postdoctoral research position in the United Kingdom.

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Alan Carey, Professor, Director, Mathematical Sciences Institute, Australian National University

Thank you for the opportunity to provide feedback on my experience at BIRS. I have been involved in both `research in teams' and in the weeklong regular workshops. In addition my collaborators, students and postdoctoral fellows have been able to accompany me to Banff. For younger researchers these visits have been of major importance in both exposing them to current research and also enabling them to begin to build their own research networks and collaborations.

My own experience has also been very positive. From my `research in teams' visit a long-term project was started with some of the other members of the team. In addition we were able to learn from experts with similar interests their views on our research ideas. Workshops have performed a slightly different function with there being naturally less time for immediate collaboration. However the opportunity to live and breathe mathematics in such a stimulating environment has made an enormous difference to my research and provided me with direct interaction with the leaders in the areas in which I am interested.

Finally I would mention that BIRS is a kind of hub for Pacific rim interactions and is of great value to Australian mathematics given that there is no comparable institute in Australia. I hope that BIRS will continue to play its vital role in mathematics for the foreseeable future.

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Frank den Hollander, Professor, Chair of Probability, Leiden University

Including the upcoming workshop on spinglasses next November, I will have organized two workshops at BIRS and participated in two others. Each workshop was a delightful experience, and each led to contacts that turned out to be fruitful later on.

For me one workshop on polymers at BIRS was crucial, because I met a large number of researchers from physical chemistry and from combinatorics whom I did not know. In my 2009 book on ``Random Polymers" (Spirnger LNM 1974, Saint-Flour lectures 2007), some of their work has been integrated, and I am maintaining contact.

I value the fact that at BIRS there is ample time for discussion, due to the relaxed lecture schedule. This is the same at Oberwolfach, but absent from most other workshops.

As an organizer I find that all I need to worry about is putting together a good program and the rest is handled smoothly and swiftly by the BIRS staff, both before and during the workshop.

BIRS has grown into a real asset for the mathematics community.

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Robin Chapman, Professor emerita of Communicative Disorders, University of Wisconsin-Madison

I was a participant in the 2006 Creative Writing in Science and Mathematics workshop at BIRS; the workshop introduced me to an extraordinary group of physicists, environmental scientists and mathematicians, science writers, playwrights, poets, nonfiction and fiction writers who were all trying to double-map the world in narrative and mathematical structures; to live in the ``two cultures" of the creative arts and scientific discipline. The interaction substantially improved the science and the writing of my poems on evolutionary change and cognition; and the accounts of the scientists writing for lay audiences, highlighting the importance of narrative and metaphor in communication in both kinds of writing. It also led to an anthology of work, The Shape of Content (AK Peters) drawn from the several years of the workshop; and a network of friendships and writer-connections that have proved enriching and invaluable. My great thanks for the opportunity; I hope you continue to offer the possibility of bringing creative artists and creative scientists together; the mix humanizes science and makes the creative writers responsible to scientific fact, and creates a third dimension of play and creative thinking.

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N. S. Narasimha Sastry, Division of Theoretical Statistics and Mathematics, Indian Statistical Institute

I had the privilege of attending a one-week workshop on ``Invariants of Incidence Matrices" during March 29 - April 3, 2009. I found the workshop very well organized, very focused, and on a very well defined topic. I had an opportunity to meet several mathematicians currently active in that specific topic and those who have contributed significantly to this topic. This excellent opportunity to share insights and concerns regarding this topic has been very useful in extending the frontiers of our understanding .

It is very clear that such workshops are very fruitful and are eminently deserving of continued support.

Regarding the centre and the facilities, nature's blessing has been munifecent and the ambience, hospitality and the arrangements at the Banff Centre are excellent. I can hardly think of any suggestions for improvement. Except that, perhaps a small snack may be made available between dinner and breakfast in the next day.

I am very thankful to the organizers for their invitation to me to participate in the workshop.

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Robert Brandenberger, Chair, Canada Research, Professor, Department of Physics, McGill University

I have been fortunate to be able to attend four five day workshops [at BIRS], one of them I was a co-organizer for. The Banff facility is perfect for such workshops. The location is perfect, the atmosphere stimulating, and the setup encourages both formal and informal interactions between participants. I have learned much more about recent developments in string theory during my visits to BIRS than anywhere else. The size of a typical workshop is such that one can productively interact with most of the workshop participants. The combination of talks and personal discussions allows one to understand a subject at a much deeper level than would be possible by listening to talks at a large conference. The fact that one dines with the workshop participants for all meals allows contacts to deepen. Of all of the conferences and workshops I get invited to, BIRS workshops for me are the most attractive and most valuable. While I was still teaching at Brown University I used to occasionally go to the Aspen Center for Physics. However, recently the cost of attending an Aspen program has increased so much that most scientists cannot afford to go. BIRS has the advantage that the cost for the participants is much less. As a consequence, a healthier mix of people can actually attend.

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Andrew Granville, Professor, Department of Mathematics, University of Montreal

Over the years I have been to many meetings at Banff. It is a wonderful location and the set up is ideal for a small and intense meeting. The surroundings are, of course, stunning, and hiking the trails with colleagues from around the world has led to many collaborations and helped to develop ideas. There is a wide range of meetings at BIRS, indeed covering all of my mathematical interests, and even some that go beyond. Perhaps the one that has been most important for me, was a meeting on Creative Writing in Mathematics a couple of years ago. I enjoy writing in mathematics, indeed I have won four international mathematical writing prizes including last year's Chauvenet prize, but had never really thought through how one could be especially creative in writing about mathematics. At this meeting there were all sorts of people taking all sorts of approaches to writing about mathematics, some rather obvious, but others quite surprising. This led me to thinking more about communication of ideas - how my success in expository writing is about understanding how to reach a wider audience, but how well does that measure up to all the ways that people communicate in other areas? To reach out further than expository writing, authors sometimes attempt a socratic dialogue (or multi-logue), usually written rather artificially, at least it seems so in these days of television and attempts to reach people through visual mediums. Through this thinking was born the idea of trying to create some sort of TV program that would incorporate the best traditions of socratic dialogue, without having a socrates-type character (i.e. every question being answered by some sort of super-expert) and using what works on TV.... What is very popular right now are crime investigations using forensic laboratories, where the forensic investigators gradually piece together the evidence, no one being too smart - can one creatively write mathematics in this way? Working with a screenwriter with whom this idea was initiated at Banff, we have now written a script, which can be read as a mathematical text, and can be read as a TV crime show. We are currently editing it and it is likely it will be first performed as a theatrical piece at the Institute for Advanced Study in December, using actors from film school in New York. I recognize this all sounds a little crazy - indeed there is, as far as I know, nothing around quite like what we are doing, and for a lot of people this sort of experimentation is uncomfortable; but I am grateful for having had the time and opportunity at Banff to come to the decision to try to do something quite so different!

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Jie Liang, Assistant Professor, School of Engineering Science, Simon Fraser University

I attended two 5-day workshops organized by the Banff International Research Station (BIRS), one in 2005 and another in 2009. They are on the same topics. They provide me a good opportunity to meet with the leading experts in my field, get to know the latest development, and discuss with them to generate new ideas. By analyzing the changes of topics in the two workshops, I can also identify the trend of the research in this field.

I hope that this unique program can be continued in the future.

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Xianguo Li, Professor, Editor in Chief, International Journal of Green Energy, Department of Mechanical and Mechatronics Engineering, University of Waterloo

I was fortunate to have the opportunity to attend the Computational Fuel Cell Dynamics Workshop held at Banff International Research Station a few years ago. The relaxed and somewhat seclusive atmosphere allow ample opportunities for the workshop attendees to network and interact, and really get to know each other well. The scientific discussion has led a fruitful and lasting collaboration with some of the other workshop attendees. Joint research projects had been initiated, quite a number of joint research papers have been published since then. The impact of the workshop is not only what we learned at the workshop, rather it is the professional connection and friendship that have developed since which would be a life-long treasure; and the good will and friendship that have developed since which have been nurturing the professional collaboration and inter-cultural understanding.

I would like to take this opportunity to thank you for your professional leadership and your vision in establishing and leading this Banff International Research Station. I'm confident that more professionals are going to benefit from your leadership and dedication for their professional career and life as well.

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Marcus Kracht, Department of Linguistics, University of California, Los Angeles

I have taken part in a workshop on the applications of mathematics to philosophy organized by Richard Zach, which has been very influential for me for I was able to meet with many important researchers and discuss with them recent ideas. The meeting was certainly the most important one that I took part in during the last five years.

The BIRS is an ideal venue for such meetings and I sincerely hope that it will continue to be funded in the way that it is.

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Hannes Leeb, Associate Professor of Statistics, Department of Statistics, Yale University

I've attended a workshop at BIRS last year, September 14-19 2008, titled `Understanding the New Statistics', that was organized by Rudy Beran, Sara van de Geer, Ian Johnstone, and Ivan Mizera. Having recently attended a workshop in Oberwolfach, Germany, I was delighted to find a similar institution in Canada. At the workshop, I was able to continue my cooperation with Benedikt Poetscher (University of Vienna, Austria), to re-connect Marten Wegkamp and Flori Bunea (University of Florida, Talahassee), Rudy Beran (UC Davies), and to meet new people, foremost among them Noureddine ElKaroui (UC Berkeley) whose research is of particular interest and importance for my own work.

I believe a place like BIRS is an indispensable part of our research environment, and strongly hope that it will receive continued funding.

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Santiago R. Simanca, Professor, Department of Mathematics, University of New Mexico

I am very thankful for the opportunity I had to participate in the workshop on Extremal Kaehler Metrics. It is a pleasure to thank the organizers and the entire local group for putting this event together. I was able to carry out some important calculations for my current work embedded in an ideal environment. As I mentioned already to Ms. Williams, the BIRS Station Manager, I was fascinated by the fact that at this Centre the humanities and sciences seem to go together, and innovation and discovery are understood amply. Our workshop took place while the Centre was filled with a large group of talented musicians from all over the world. During the week, I managed to attend a concert at the Centre, and that in itself was inspirational to carry on my work. It was a pleasure to do mathematics in that environment. I hope that these ideals the Centre has to model its function remain for years to come.

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Marianne K. Korten, Professor, Department of Mathematics, Kansas State University

I participated in the BIRS Workshop 07w2125 Diversity in the Mathematics and Scientific Community I and II. The result of this workshop is a webpage collecting resources that everybody is welcome to use regarding improving the situation of women and minority faculty/instructors/graduate students at math departments. Plus a network of people, many with more experience than myself.

I benefited greatly from the exchange of ideas at that workshop, and form the people I met that are now part of my network. To begin with, it gave me a source of people to invite for an endowed lecture series or distinguished women mathematicians my department has. I invited at least two people I met at the workshop that impressed me. Further: I have since been promoted to full professor. As a result I felt I have the ``room" to seek service positions in my department from which I expect to have an impact (my department had no female faculty whatsoever 9 years ago; the only minorities were Asian males). In this way, I became a member of the Graduate Program Advisory Committee and interim director of the ``I-Center" (VIGRE-type appendix of our department focused mostly on undergraduate research and getting students ready for graduate school). I wanted these positions to improve our track record with female and domestic students, in order to improve our chances of getting institutional grants. The network from the workshop contains colleagues with experience in these areas whom I plan to exchange best practices with. I also became a member of the College of Arts and Sciences Diversity Committee. This hasn't been very productive so far in spite of my efforts. The best thing was to host the first mathematician speaker in the A & S Diversity lecture (Rodrigo Banuelos). Via this lecture I got in touch with numerous minority students, and other minority and first generation in college supporting campus organizations. I will cooperate with these organizations as I-Center director. I this position I am also cooperating with the Multicultural Engineering Program, and in touch with Native American student organizations. I served again on the AWM nominating committee and had a nice source of people to nominate taken from the network the workshop produced.

I hope this will be of use for your report. It was great to have the opportunity to join this workshop. Banff is a great place to facilitate all this!

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Julius Ross, Researcher, Professor, Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, University of Cambridge

I very much enjoyed the recent conference I attended on extremal metrics. It gave me an opportunity to spend time with existing colleagues, as well as meet new people in the field. It also gave me an opportunity to work on an existing project with a collaborator, and possible start another one. The conference center and the organisers did a wonderful job, and the conference ran very smoothly.

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Stanislav Jabuka, Associate Professor, Department of Mathematics and Statistics, University of Nevada, Reno

I have had the pleasure if visiting BIRS three times in the last six years and each of my visits was a great pleasure, both professionally and personally. The atmosphere of research and collegiality is hard to compare to any other place. I always leave Banff inspired and motivated to work on new ideas. One of my long-term collaborations started at one of these conferences.

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Rene Boel, Professor, Department of Electrical Energy, Systems and Automation, Ghent University

As a participant to a short (3 day) workshop in BIRS I can only express my sincere appreciation for the opportunity I and my colleagues were given to discuss in a small but very motivated and very focused group some novel research topics (in the area of distributed discrete event systems control in our case). The atmosphere at the meeting was perfect for intensive exchange of new ideas. It surely helped me a lot and started some new collaborations with colleagues I knew a little bit beforehand, but whom I know a lot better now.

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John T. Baldwin, Professor Emeritus, Department of Mathematics, Department of Statistics, Department of Computer Science, University of Illinois, Chicago

I found the meeting very valuable for renewing and making mathematical connections. Here are some examples.

I spoke in Banff about the preservation of `stability properties' when a structure is expanded by naming a predicate.

Chris Laskowski had an insightful response to one of the questions. He, Baizhanov and I are continuing work on this topic. Baizhavov spoke on the work at the Asian Logic Conference in Singapore; he and I made some further advances.

Artem Cernikov has announced a solution to a second problem I posed: showing that naming an order indiscernible sequence preserves n.i.p. under certain smallness hypotheses. This is posted on the archive.

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Andrea Maffei, Researcher, Department of Mathematics, University of Rome

I went to BIRS in September 2007, for a conference on algebraic groups, the title of the conference was: ``Group Embeddings: Geometry and Representations".

This had been a very nice conference. Particularly interesting for me were a couple of talks with F. Knop about the tensor category of ``representation of $S_t$" with t not an integer constructed by Deligne. Although I couldn't solve the problem which grew out of this discussion, it opened for me a new area of interest related with finite groups of Lie type.

Also important for me was a conference by D. Luna, on the classification of wonderful varieties. This theory allows for the generalization of the more general situation of spherical varieties some results obtained for symmetric varieties, which have been my main research interest in the last years. Some results in this direction has been obtained by my PhD student Jacopo Gandini. The seminar of Luna in this conference was important for me in this line of research.

Finally the organization was perfect and the place very nice.

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Tom H. Koornwinder, Professor, Korteweg-de Vries Institute for Mathematics, University of Amsterdam

In the acknowledgement at the end of my paper

T.H. Koornwinder, Zhedanov's algebra AW(3) and the double affine Hecke algebra in the rank one case. II. The spherical subalgebra, SIGMA 4 (2008), 052, 17 pages; arXiv:0711.2320v3 [math.QA]

I wrote:

Some of the results presented here were obtained during the workshop Applications of Macdonald Polynomials, September 9-14, 2007 at the Banff International Research Station (BIRS). I thank the organizers for inviting me.

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Marcus Mueller, Institute for Theoretical Physics, Georg-August-Universität

I am looking very forward to participate in your scientific program in the next year. I strongly believe that instruments like the BIRS are vital for a efficient and enjoyable scientific exchange and foster collaboration among a broad spectrum of scientists. I am looking very forward to the workshop on ``Self-Assembly of Block Copolymers: Theoretical Models and Mathematical Challenges" in May 2010.

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Russell Lyons, Professor, Department of Mathematics, Indiana University

I was in a conference in 2005 and an FRG in 2009. The conference led to a collaboration that resulted in 2 papers; it would not have occurred otherwise. The FRG led to new contacts and a wealth of questions to work on. The FRG helped to unify disparate threads of research in various communities. This inspired a new result I obtained while I was there.

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Paul Higgs, Professor, Department of Physics, McMaster University

I have attended only one workshop at BIRS, but I am aware of the diverse program of ongoing activities. The research station has an excellent and unique atmosphere in which scientific discussions and collaborations can be carried out. At the workshop I attended in 2008, I met several old colleagues and got to know a lot of new ones. The discussion was at a detailed and focused level on particular problems, and time was available to discuss these problems properly, in a way that would not usually be possible at conferences. I think that the level of scientific activity at BIRS is on a par with the best international research schools and conferences around the world. This facility is an important asset to the Canadian research community, and I hope that it will continue to be fully supported by the research funding agencies in future.

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Hans-Christoph Grunau, Professor, Department of Mathematics, Otto-von-Guericke University Magdeburg

I enjoyed my stay in Banff very much during a workshop in summer 2006 organised by Frederic Robert, Emmanuel Hebey and Matthew Gursky. It's this sort of workshops which are the basis for an efficient and successful scientific work. In particular I enjoyed discussions with Alice Chang, Paul Yang, Emmanuel Hebey, Yuxin Ge, Michael Struwe and, last but not least, with Frederic Robert. With Frederic Robert, this workshop was part of our collaboration which finally resulted in the following paper: http://www.springerlink.com/content/07670t6m778x0l37/

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Matt Hedden, Assistant Professor, Department of Mathematics, Michigan State University

A few years ago, I was asked to write a testimonial for BIRS and gave a description of the influential nature of my first BIRS experience, which occurred during my third year in graduate school. That conference, being my first, was instrumental in my development as a mathematician and ended up inspiring my first original theorem (which ultimately became a large part of my thesis). It has been five years since that conference, and I have been grateful for the opportunity to attend several (3) five-day workshops during these years. All of these experiences have been influential to my mathematical development. The most recent of these conferences, ``Interactions of Geometry and Topology in dimensions 3 and 4", took place in the winter of 2009 and was extremely fruitful. In addition to the excellent panorama of the field provided by the speakers, I had the opportunity to interact with a wide variety of researchers from across the world. In particular, the involvement of a number of participants from Europe and the Middle East was extremely important (as most of the conferences I attend are unable to accommodate such an international group). Indeed, this was one of the most successful conferences I have attended and it contributed not only to my breadth and overall knowledge but also led to a collaboration with Yi Ni that recently culminated in a joint paper ``Manifolds with small Heegaard Floer rank" available at http://arxiv.org/abs/0906.4771. Our collaboration is, in my opinion, an example of the effectiveness of the BIRS environment and the excellent oganizational abilities of all involved. BIRS has played a key role in all phases of my research life to date, and I sincerely hope that it will continue to serve that purpose in the years to come. I believe BIRS to be on par with, or better than, any of the many research institutes and conferences that I've had the opportunity to participate in.

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Saurya Das, Associate Professor, Department of Physics and Astronomy, University of Lethbridge

I had attended two two-day meetings at the BIRS, in August 2003 and May 2005, both co-organised by the Institute of Theoretical Physics, University of Alberta. The meeting had been quite useful to me. I presented an invited talk and discussed with several colleagues during each meeting. I hope there are more such meetings on fields of my interest (Quantum Gravity/Theoretical Physics) in the near future which I can attend.

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Dan Kabat, Researcher, Theoretical Physics, Lehman College, City University of New York

I attended the program ``Emerging directions in string theory" in June 2008. The workshop provided a valuable opportunity to interact with several close colleagues I hadn't seen in a while. Just to pick an example, at the time I was working on string gas cosmology, and during the workshop I had several discussions with Robert Brandenberger who was one of the originators of the field. As another example, I got to hear about some important new developments in gravity / gauge duality from Jan de Boer while making an attempt on Mount Rundle. Many other physicists also benefited from the workshop, and I've seen it mentioned in several papers. I'm thinking in particular of discussions between Wati Taylor and Joe Polchinski that I know were important in Wati's recent work on the K3 landscape.

Overall the workshop was very well organized and run. Banff is justly famous for its workshops, which play an important role in my field, and I look forward to returning to Banff soon.

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Daryl Daley, Professor, Centre for Mathematics and its Applications, Mathematical Sciences Institute, Australian National University

I participated in a weeklong programme at BIRS about four years ago (the timing is almost exactly four years to the day as I write). The occasion was a celebration of David Brillinger's 65th birthday, but less precise (as I recall) in terms of that day. The conference presentations covered a wide range of David's interests, and speakers did of course branch widely beyond that.

One talk in particular sticks in my mind, given by Adrian Baddeley, known to me as a fellow Australian, and indeed, a fellow graduate from the University of Melbourne, albeit a couple of decades apart. He spoke about his work, with others, that was subsequently published as a read paper with Discussion in the Journal of the Royal Statistical Society Series B (Methodological), on practical analyses of spatial data, in particular of point processes. It was then, and still is, at the forefront of this difficult field. Now in the last twelve months I have been at the more mathematical side of spatial statistics, without any point process emphasis, but in the guise of space-time (or, spatial-temporal) statistical analyses: Baddeley's work has been a fascinating and insightful approach to this topic, for which my background (and link to Brillinger) has been via point processes. (This current work concerns preparation, jointly with two colleagues in Spain and Germany, of a graduate-level book manuscript for publication by Springer, on Space-time modeling.)

To me, I refer to just two connections -- of both Baddeley and me to Brillinger via point processes -- that, put together at Banff, exemplify how research at the theoretical level need not be immediate in its aftermath but, given gestation time and sometimes other chance events, evolves through amassing related people and subjects to advance the subject-matter and science in general.

I have other on-going work with Peter Glynn, another Canadian resident in USA at Stanford University and who was at this `Brillinger gathering' meeting. That work too has a long gestation period: it is being restarted now because of meeting with a younger researcher six weeks ago at the Polish Mathematical Society's research and conference facility at Bedlewo.

Meetings such as this Brillinger occasion at BIRS, play an invaluable role in fostering research interaction in mathematics, and especially in bringing together both young and old to sit in the same lecture theatre, around the same dining table, in the same common room, or hiking the same trail outdoors. For me, it remains a priority that I participate when invited to such gatherings, whether at Banff or Bedlewo or Oberwolfach in Germany, despite having to travel from down under.

I do hope that BIRS continues into the next decade.

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Joan Hutchinson, Professor, Department of Mathematics and Computer Science, Macalester College

I have been involved with three events at BIRS during the past four years, and all were excellent. My first visit was in the summer of 2005 to attend the ``Renaissance Banff, Bridges Conference", where my husband's work in mathematical snow sculpting was being presented. I was fascinated by the talks and gained a lot for my subsequent teaching, showing ``bridges" to other disciplines and cultures. In October, 2006, I was an invited participant in a workshop in Topological Graph Theory, run by PIMS at BIRS, which was really fantastic! All the leaders of the field were there and I met with some new, young researchers. I worked on problems of ``list-coloring" with Professors M. Albertson, B. Richter, and C. Thomassen, which resulted in my paper ``On list-coloring outerplanar graphs", J. Graph Theory 59 (2008) 59-74, and is central to my on-going work on variations on list-coloring suggested by these three. On current project is with a researcher M. Axenovich at the Iowa State University and her graduate student, on a conjecture of Albertson. Another is a project with researchers from Germany, Hungary, and the U.S. on a conjecture of Richter, which he made at BIRS in response to my current research. It was an excellent learning and working environment for us and I really think represents the best sort of conference: small with a group of diverse mathematicians, but interested in a common area, with good opportunities to work together. After that I became a member of Program Committee for the first meeting of the Canadian Discrete and Algorithmic Mathematics conference (CanaDAM) to be held in Banff, Canada, May 28-31, 2007, but unfortunately I could not attend that meeting. The reports were that it was excellent, and the first in a series of alternating-year meetings in Canada. I've been very pleased to work with BIRS and hope to be able to do more in the future.

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Guido Kanschat, Assistant Professor, Department of Mathematics, Texas A&M University

I participated in the workshops on discontinuous Galerkin (DG) methods in November 2007 and on saddle point solvers (SPS) in April 2009. In both cases, BIRS provided a perfect atmosphere for presentations and discussion. The fact that workshops are small and participants meet for a whole week, including meals and evenings is very stimulating for learning things from personal conversation not as readily obtainable in presentations. Additionally, the format allows participants to develop personal relations to other researchers from Canada and all over the world. Both workshops featured the internationally leading researchers of the respective fields updated me on the state of the art. From the first workshop resulted a new collaboration with Beatrice Riviere which resulted in a publication soon to be submitted and plans for a joint research project. The SPS workshop gave me many new insights into preconditioning methods for problems I am currently solving for my research and I started implementing them; preliminary results show a potential to boost performance of my simulations and thus open alleys to more advanced topics.

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Jiri Spurny, Associate Professor, Department of Mathematical Analysis, School of Mathematics, Charles University

I was a participant of the Northwest Seminar on Functional Analysis held in January 2005. It was a very useful an pleasant experience since I had the opportunity to meet several distinguished mathematicians and visit their lectures. Also, their comments and remarks to my work helped me substantially because I obtained suggestions how to apply my results in other areas of mathematics.

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Andreas Baudisch, Professor, Department of Mathematics, Humboldt University of Berlin

I attended the modeltheory meeting this February. I am an organiser of Oberwolfach-Meetings in Modeltheory in Germany. Oberwolfach is similar to Banff. These kind of meetings are of great scientific value, since they create a special very productive atmosphere. People come closer in contact as in greater and more official meetings. In both institutes spontan sessions play an important role. My students Artem Chernikov and Pierre Simon (another participant) started the solution of a problem of Baldwin Benedikt in Banff.

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Tine Reimers, Special Assistant to the Provost for Faculty and Program Development, Office of the Provost, University at Albany

I am pleased to report on my experience at the BIRS station. I participated in a 2008 Workshop on ``Mentoring for Engineering in Academia II". It was a very useful experience for me, allowing me to make new contacts from across the US and Canada in the realm of mentoring in the sciences and engineering. The contacts I made at that workshop are still active and we continue to exchange ideas for how to increase the number of women and underrepresented minorities in academic sciences and engineering, and how to mentor them for success. The workshop resulted in a ``proceedings" which collected the best ideas, conversations and guiding documents for mentoring that resulted from participation of a wide range of attendees: from PIs on ADVANCE grants, University Presidents, graduate students, faculty developers, to Deans and Professors of science and engineering, all focused on increasing participation and diversity in the sciences and engineering. It was well worthwhile as a place and time to exchange best practices and to develop new directions for mentoring. I strongly believe that BIRS offers a valuable space for in-depth conversations that can contribute to the progress of science and engineering in the US and Canada.

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Martin Roetteler, Researcher, NEC Laboratories America, Inc.

I attended two BIRS workshops in my scientific career: one on quantum computing in 2002 and one on operator theory and quantum information in 2007. Both workshops were extremely helpful for me. Let me give a little bit more detail about these two experiences:

The 2002 quantum computing workshop was tremendously helpful for me as a young research who had just finished his PhD the year before. There was ample opportunity during the workshop to make new contacts and to deepen the relations I had with some of the attendants. I remember that we had many discussions in small groups (3-4 people) in small break-out rooms. I think that one of these contacts actually might have helped to find my current employment! Also, back in these days it was very helpful for me to see in which direction the community is going and what the hot topics are. As almost all experts in the field were there this was the perfect opportunity to learn about these things. The workshop probably contributed to help me make a decision about continuing research in the field of quantum computing.

The 2007 workshop was an extremely well organized workshop, attended by some of the most prominent researchers in the field of quantum information theory. It was amazing how open the tmosphere was and how freely people talked about open problems and challenges. The organizers Mary-Beth and David compiled a long compendium of open problems in the field, a unique source of inspiration for students and researchers. There were talks until late in the night, everybody being genuinely interested in recent results of the other participants.

Summarizing, to me the Banff research station is a unique place. Even though so far I only had the opportunity to be there twice, those workshops were very memorable and important for my research.

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Éric Marchand, Professor, Department of Mathematics, University of Sherbrooke

I participated in a BIRS workshop in 2006 bringing together statisticians and physicists in discussion and debate concerning a series of contemporary problems in high energy physics. All my local expenses were paid, and I paid my travel expenses.

The facilities were first rate, but more importantly, I was privileged to take part in these scientific exchanges. Some of my work had already been influenced by some potential applications in physics, and I was able to disseminate my recent research findings but I was able to get a much better understanding by participating in the workshop. I also learned from meetings with statistical colleagues.

Without a doubt, this investment was more beneficial than a large majority of conferences that I have attended. I have had two students (one M.Sc, one Ph.D.) work directly on problems that emanated from the workshop.

I look forward to visiting BIRS again and I am envisaging submitting a proposal to organize a workshop on contemporary problems in statistical Bayesian analysis and decision theory.

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Robert Coleman, Professor, Department of Mathematics, University of California, Berkeley

I have attended three workshops at BIRS, one of which I organized. They have all been very helpful to my research and that of my students' research. I learned of the work of Payman Kassaei at one and Stephan Wewers at another. Also I had a very interesting conversation with Kevin Buzzard at the former. I think BIRS provides a valuable service to the mathematical community.

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Keith A. Baggerly, MD Anderson Cancer Center, University of Texas

My experience with the Banff workshops was quite positive.

I work in genomics, and I got a chance to interact with several individuals who were working with technologies I was either struggling with or knew I would soon be encountering. For example, I was and am working with Illumina SNP assays and trying to assess copy number changes in cancer cells. I got to meet and talk with Simon Tavare and Natalie Thorne, who had been working with this data on a different level than I had, and to learn about some R packages for processing such data that I was unfamiliar with. I also got to talk with Jian-Bing Fan from Illumina about the nature of their platform and about some ofits limitations. And I got to talk with Rafa Irizarry about some steps I had made in terms of automating the analysis which one of his postdocs was subsequently able to exploit.

I got to talk with several people about the potential for new high-throughput sequencing technologies, which they had begun to work with and which I'm working with now. This has affected where I'm looking for some automatic tools, some of the QC steps I make automatically, and some of the background literature I've tracked down.

Conversely, I got to present more basic work of my own on the need for more attention to reproducible research in high-throughput biological studies, which led in turn to others requesting reports and guidelines I had developed.

The Banff environment was conducive to this type of interchange, as I find small focused meetings more effective in this regard than very large ones. I would say that most attendees knew a few of the others coming into the meeting, so there was a great deal of cross-talk and introduction.

My experience with the Banff workshops was quite positive.

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Sebastien Ferenczi, Researcher, Institute of Technology, Luminy Campus

The questions I was asked during my lecture at BIRS in June 2008 were the source of a major improvement in the following paper, which is now accepted for publication in Journal d'Analyse Mathematique Structure of $k$-interval exchange transformations: induction, trajectories, and distance theorems, by S. Ferenczi and L.Q. Zamboni With my thanks to BIRS.

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David Balding, Professor of Statistical Genetics, Department of Epidemiology and Public Health

I'm happy to add my name to supporters of BIRS. I appreciated very much my invitation to the Bioinformatics, Genetics and Stochastic Computation workshop in July 2007. The intellectual level of the meeting was at the forefront internationally, and the salubrious environment was very conducive to networking and to serious discussions of research ideas.

It is the nature of almost all academic research that developments are incremental, and I cannot attribute any specific breakthrough or new research direction to my time at BIRS (I'm at the mature stage of my career where I have too much unfinished work; new research directions or collaborations are the last thing I need). Nevertheless I can remember specific seminars and discussions that were very beneficial to my thinking.

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Philip Holmes, Eugene Higgins Professor, Department of Mechanical & Aerospace Engineering, Princeton University

I attended the first BIRS workshop on Creative Writing in Mathematics and Science in 2004, and hope to attend the upcoming one in 2010 (I could not attend in 2006). The gathering of mathematicians, scientists and writers was unusual, and the discussions and sharing of works in progress were very stimulating. I rarely get to mix my lives as an applied mathematician and poet. BIRS enabled this, and rekindled my attempts to mix it up on paper.

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Antoine Henrot, Director, Elie Cartaan Institute, Professor, Ecole des Mines de Nancy

I participated in a meeting on ``Geometrical Inequalities" in June 2007. This was a very nice meeting. I discussed with several colleagues that I have never met before. Following a beautiful talk given by A. Fusco, I have begun a collaboration with Prof. B. Kawohl which is still active on quantitative isoperimetric inequalities. With my ``french" experience, I must say that the Banff Center is as useful as our CIRM at Luminy or MFO at Oberwolfach.

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Klaus Hulek, Professor, Vice-President for Research, Leibniz Universität Hannover, Germany

I took part in one of the first ``research in teams" activities in March 2003. The group which met at this time were David Eisenbud, Mark Green, Sorin Popescu and myself. This meeting gave us the chance to make essential progress with our joint project on syzygies of miniml degree algebraic sets. The final result of our collaboration were the papers

MR2275024 (2007j:14078) Eisenbud, D.; Green, M.; Hulek, K.; Popescu, S. Small schemes and varieties of minimal degree. Amer. J. Math. 128 (2006), no. 6, 1363-1389.

MR2188445 (2006m:14072) Eisenbud, David; Green, Mark; Hulek, Klaus; Popescu, Sorin Restricting linear syzygies: algebra and geometry. Compos. Math. 141 (2005), no. 6, 1460-1478.

The collaboration in Banff was essential in achieving these results and we are very grateful for the opportunity and the fantastic working conditions which were provided by BIRS.

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Joseph J. Kohn, Professor, Researcher, Department of Mathematics, Princeton University

My experience in the workshop I participated in at BIRS was very positive. The mathematical discussions have been very helpful in my research and the meeting reinforced my contacts with mathematicians with similar interests. Beyond the great value of the workshop to my own research it was invaluable to the younger participants. The inspiring natural setting, the facilities, and the smooth organization all contributed to a very fruitful and rewarding experience.

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Julia Gordon, Professor, Department of Mathematics, University of British Columbia

I have been to BIRS for workshops twice, and I remember the both times as somewhat pivotal moments. The first time, I was a graduate student, and this was the first workshop in my current field of research that I attended. It was a wonderful opportunity to get a sense for the current research, and to meet for the first time the people that I've been meeting in conferences regularly since then. I always sense some shared warmth when you meet someone after some years, and they say ``yes, we met in Banff, remember?" But even with emotions and networking aside, I don't know, maybe it was a lucky coincidence, but it was during that workshop in Banff that I found the last missing piece of my thesis problem, that I'd been searching for months before. I cannot say that some talks or communications supplied it directly, but certainly the general atmosphere helped.

The second time I attended a workshop in Banff, I got the first chance to meet and talk to the founders of the theory that I have been using. This theory was being developed very fast at that time, by people in Europe. If not for that workshop, I probably would have had to wait a year for their papers to appear, to learn of the most recent developments. Since that workshop, I've been much more in touch with that community, and without that my current work would not have been quite possible. I probably would have got in touch with them somehow eventually, but the workshop was just a perfect opportunity.

In short, I've always been really grateful for both opportunities to visit BIRS.

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Peter L. Erdos, A. Renyi Institute of Mathematics, Hungarian Academy of Sciences

Indeed, I have the luck to participate in Banff, at BIRS on the workshop Infinite Graphs, Sunday, October 14 to Friday, October 19, 2007. (07w5117). I enjoyed it tremendously: on one hand side the environment is just wonderful, on the other side I found the scientific program refreshing and extremely useful. While I have known the majority of the participants earlier, it gave me the opportunity to get know several colleagues. I also learned a lot about infinite graph theory as well as on the homomorphism posets of finite graphs. So if I would be offered to come back to Banff I would take the opportunity without any delay or hesitation.

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Stu Whittington, Researcher, Department of Chemistry, University of Toronto

Since BIRS began its operations I have attended three 5-day workshops. In my view each of these was enormously successful. They brought together scientists and mathematicians from different communities who all had common research interests but attacked problems with very different techniques. At each meeting that I attended I renewed old acquaintanceships, met new people working on similar problems, and learnt about open problems that I hadn't come across before. Each of these workshops had a positive affect on my research and led me to work on new problems and to investigate new research areas. BIRS is making a major contribution to Canadian mathematics and science.

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Pierre Arnoux, Equipe Dynamique, Arithmétique et Combinatoire Institut de Mathématique de Luminy

I participated recently in a Banff workshop (Topological Methods for Aperiodic Tilings 08w5044, October 12 to October 17, 2008.), coming from the university of Marseille (France).

The workshop was very useful, and I learnt a number of things, and established new contacts. In particular, I discovered in this workshop that several French researchers were working independently of me on topics related to my research; since they were coming from a different background, I had not had an occasion to meet them yet. We found that we had common interests, and this led to a research project, which has recently been funded for 4 years by the French research agency, and which will be our main research activity in the coming years; this would certainly not have taken place without the Banff workshop.

I very much hope that BIRS will continue in the coming years, and that I will have again the possibility to enjoy its hospitality; it is a unique research environment.

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Petr Hlineny, Associate Professor, Department of Computer Science, Masaryk University

I like the scientific idea of BIRS very much, the station creates a very encouraging cooperation environment, especially at thematic workshops. I have participated at the workshop 06w5067, where I met together many of the mathematicians with whom I have common interests (and such meetings are quite rare). The following paper directly originated from discussions at that workshop (it acknowledges the workshop).

Petr Hlineny: New infinite families of almost-planar crossing-critical graphs. Electronic Journal of Combinatorics 15 (2008), #R102.

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Jorge M. Pacheco, Professor, Department of Theoretical Physics, Department of Applied Mathematics, Universities of Lisbon and Minho,

I attended an International Conference on Evolutionary Game theory which took place at BIRS, June 2006, and this is one of the best conferences I have attended that year. I am aware that BIRS will be hosting another event of this kind in 2010, and I am looking very much forward to participate. In 2010, as in 2006, the organizers of the events are world top mathematicians, and the quality and impact of the event extends well beyond mathematics - I believe these are unique events which benefit tremendously from the privileged environment at BIRS. The atmosphere favors open discussions and new acquaintances. To me, these contacts have fostered new projects and collaborations which would have never taken place otherwise. As a result, I have started International collaborations with people I met at BIRS in 2006, out of which a couple of papers have been published so far. I hope BIRS will meet in 2010 the high expectations I built based on past experience. And I hope that BIRS will remain a major centre for Mathematical events of worldwide impact.

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Stewart Shrpiro, Professor, Department of Philosophy, Ohio State University

I attended a conference at BIRS, and had a wonderful time. The facilities were fantastic. Besides being located in one of the most beautiful parts of the world, the venue stimulated an exciting interaction among the delegates.

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Daniel Coombs, Associate Professor, Mathematics Deputy Director, Institute of Applied Mathematics, University of British Columbia

I recently attended a BIRS workshop (May 17-22, 2009) on mathematical modeling of infectious diseases. This was my second experience at BIRS (last time was back in 2003). It was an excellent workshop where I was able to have in depth discussions with previous and current collaborators, as well as learn more about research I was not so familiar with. Conversations I had at this meeting have had a direct impact on my research (even though it has been only a few weeks since the meeting) and I have established a new collaboration as a result. I found the whole experience of attending the workshop to be very stimulating and I am planning to submit a proposal to BIRS for the 2011 season.

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Yasuyuki Kawahigashi, Professor, Department of Mathematics, University of Tokyo

I have stayed at BIRS once for ``Focused Research Groups" and twice for ``5-Day Workshops". They were all excellent and stimulating experiences.

In the FRG program, I met young people in different, but related research topics and new interactions with them were highly exciting and useful for my research after that. This was in 2006, and my research direction after that was much influenced by this event.

In the two workshops in 2006 and 2008, I met many young postdocs and students, as well as established researchers I know well. It was very nice to meet active young generations, mainly in the North America, in this way, relations with our group in Japan became closer.

BIRS gives a truly precious research opportunity as well as the Oberwolfach Institute in Germany, which is more European while BIRS is more Pacific. I definitely hope BIRS will continue this successful enterprise in the future.

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Odo Diekmann, Professor, Centrum voor Wiskunde en Informatica, Utrecht University

I (Utrecht University, the Netherlands) attended the following meeting :

Dynamics of Structured Populations, April 20-25, 2008

and this was very useful for the following reasons :

- as managing editor of the Journal of Mathematical Biology, I need a broad overview, not just detailed knowledge of a small field; the workshop really helped to maintain and broaden this overview

- while working on a new edition of my book (with J.A.P. Heesterbeek) on epidemic models, it became clear that for a particular subject (the sign equivalence of $R_0$ - 1 on the one hand and r on the other) we needed a much improved presentation and proof. During the workshop I had many conversations (mainly with Horst Thieme but also with some other participants) about this topic, and these were tremendously helpful.

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Vivek K Goyal, Esther and Harold E. Edgerton Associate Proffessor, Department of Electrical Engineering, Massachusetts Institute of Technology

I am writing to assert that BIRS has fantastically served its purpose as a place to bring together groups of people - who would not necessarily meet otherwise - to work together to advance the frontiers of research.

I have participated in two BIRS meetings. These meetings comprise two of my four best work weeks in the past five years. They introduced me to many researchers, and the residential environment facilitated a lot of valuable discussions. In particular, these meetings drew me back to frame-related research; in the past three years the majority of my research has been related to frames, including sparse approximation for MRI excitation design and many results in compressed sensing.

BIRS has been a great resource for the mathematical sciences research community, and I hope that it is able to continue to operate in a similar manner.

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Anthony Davison, Professor, Department of Statistics, Ecole Poytechnique Federale de Lausanne (EPFL)

I attended a very stimulating workshop at BIRS on the statistical problems in particle physics, which led to a very interesting collaboration with a younger colleague. We ended up publishing our work in a prestigious journal, and I hope it will make a substantial impact on the problem we tackled, though it is a little too early to tell. Thus my brief visit to BIRS was a very good experience with a most positive outcome. I therefore hope strongly that further funding will be forthcoming to continue the good work.

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Dan Zuckerman, Associate Professor, Statistical Mechanics of Proteins, University of Pittsburgh

Getting to confer closely with top scientists from around the world, who are enticed by the beautiful surroundings, was a big help to me. If not for BIRS, I would not have met many of these people. The meetings also helped me to appreciate what had previously seemed minor aspects of research problems I was pursuing.

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Aldo Conca, Department of Mathematics, Department of Computer Sciences, University of Genova

I have been at BIRS twice and in both occasions I have enjoyed my visit a lot. I had the opportunity to meet mathematicians from other fields and to start new discussions and new collaborations. In particular, two of my recent papers are about research projects that have been stimulated by my first visit at BIRS in 2003. Also, my second visit at BIRS in 2006 gave me the opportunity to present results about integrally closed ideals from a modern prospective. My recent interest on syzygies have been stimulated by that meeting which was organized by I.Peeva and M.Stillman, two of the world experts of the subject.

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Laurent Desvillettes, Professor, Ecole Normale Superieure de Cachan & Institut Universitaire de France

I wish indeed to express my gratitude to BIRS, which I visited a few weeks ago, and which has enabled me to meet colleagues from the American continent whom I have not so often the occasion to discuss with. Thanks to the relaxed but hard-working ambience of BIRS, I had in particular very fruitful discussion with A. Vasseur (Univ. Texas at Austin) and Y. Guo (Univ. Brown) which may lead to future collaborations and, hopefully, to important results (it is of course too early to know that for sure). Thanks again to BIRS for giving this opportunity.

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Christian Ausoni, Professor, Mathematical Institute, University of Bonn

I had the chance to attend the workshop ``New Topological Contexts for Galois Theory and Algebraic Geometry", March 9 - 14 2008.

This workshop brought together mathematicians working in topology and algebra, and was a great opportunity to meet people working in new developments inspired from classical Galois theory.

All the practical issues were very efficiently taken care of by the staff, and we could concentrate on mathematical discussions and research. As acknowledged, the following paper is based on discussion and research at this workshop.

http://www.math.uni-bielefeld.de/documenta/vol-13/22.pdf

I am very grateful to the BIRS for making this possible.

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Jessica Sidman, Assistant Professor, Department of Mathematics and Statistics, Mount Holyoke College

I am happy to write about my experiences at BIRS. The setup at Banff is ideal, and especially helpful for young mathematicians. Let me explain what I mean below.

As a young person, I found it a bit intimidating to introduce myself to more established mathematicians. At large conferences in cities, I would most often choose to go for meals with other young people. But, at Banff everyone stays in the same building and it is more natural for mathematicians at all different points in their careers to mingle at meals. I feel that conferences at BIRS and in other similar conference centers have been really important in helping me to feel comfortable with more senior mathematicians socially and mathematically.

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J.-L. Colliot-Thélène, Professor, Department of Mathematics, Université Paris-Sud

Let me point out the paper

arXiv:0902.3721 Title: On the Brauer group of Enriques surfaces Author: Arnaud Beauville

which is an outcome of a problem session during BIRS Workshop 08w5083 Arithmetic of K3 surfaces.

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Noriko Yui, Professor, Department of Mathematics and Statistics, Queen's University

In the last decades and half, the world has seen explosive interactions between Number Theory, Arithmetic and Algebraic Geometry, and Theoretical Physics (in particular, String Theory). To name a few, the classical modular forms, quasi-modular forms, and Jacobi forms appear in many areas of Physics, e.g., in mirror symmetry, topological quantum field theory, Gromov-Witten invariants, conformal field theory, Calabi-Yau manifolds and in block holes. Also modularity questions of Calabi-Yau varieties and other higher dimensional varieties in connection with Langlands Program are getting considerable attention and feedbacks from physics. Zeta-functions and L-series enter scenes at various places in physics. Via renormalization, Feynman integrals are related to multiple zeta-values, and purportedly to motives. Calculations of the energy and charge degeneracies of black holes lead surprisingly to Jacobi forms and Siegel modular forms.

Though mathematicians (number theorists) and physicists (string theorists) have been working on modular forms, quasimodular forms, Jacobi forms and more generally automorphic forms in their respective fields, there have been very little interactions between the two sets of researchers, although with some exceptions. In other words, both camps have been living in parallel universes.

There have been strong desires among mathematicians and physicists for more workshops directed to the areas of number theory and physics at the crossroads. A series of workshops have been organized responding to that demand, and in fact, the proposed workshop is the fifth in this series. In fact three of the past workshops were held at BIRS. The last workshop at BIRS in 2008 brought together researchers in number theory, algebraic geometry, and physics (string theory) whose common interests are centered around modular forms. We witnessed very active and intensive interactions of both camps from early mornings to late nights. We all felt that all things modular have came together at BIRS from both sides: number theory and physics (in particular, string theory). At the end of the workshop, all participants felt that both camps have finally crossed boundaries and established relatively comfortable rapport. This has led to very strong desire to have the next BIRS five-day follow-up workshop in 2011. BIRS has presented the ideal platform for mathematicians and string theorists to engage in our common endeavor.

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Alvaro Rittatore, Professor, Centro de Matematica, Universidad de la Republica

Please keep doing this wonderful job.

I have participated in only one meeting at BIRS until now (on algebraic monoids and related topics). It was a wonderful (and unique) opportunity to meet (almost all) the top specialists on the field at the same time. In may case, I met many of them for the first time at BIRS. As a consequence, the academic exchange was very intense. Some very interesting research subjects were proposed, and further collaborations were coordinated. In my particular case, as a collaboration that begun at the meeting, I have wrote 3 papers (with Lex Renner, whom I met for the first time there), and a significant part of my ``work in progress", has its roots in the exchange made at BIRS. I think the best resume I can give about my thoughts is the answer I gave to a colleague when asked about the meeting: ``I would really like a facility like BIRS in South America."

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Martin Kruczenski, Assistant Professor, Department of Physics, Purdue University

I participated in the workshop ``Gauge Fields, Cosmology and Mathematical String Theory", held from Sunday, February 1 to Friday, February 6, 2009. It was a great experience for me from the scientific point of view. It allowed me to get acquainted with the latest developments in the field and also to present my own research. Thanks to that, I wrote a recent paper

L. Freyhult, M. Kruczenski and A. Tirziu, ``Spiky strings in the SL(2) Bethe Ansatz,'' arXiv:0905.3536 [hep-th]. to appear in the Journal of High Energy Physics.

The project was motivated by talks with other participants such as J. Minahan and K. Zarembo.

I believe the BIRS Center serves an important role for physics in Canada and the US, similar to the role played by the Aspen Center for Physics. It certainly deserves all the support received over the years and I sincerely hope it continues playing that role in the future.

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Benoit Charbonneau, Professor, Department of Mathematics, Duke University

I participated in one program at BIRS so far, organized by Spiro Karigiannis, Gordon Craig, et al. (08w5039 Special Structures in Riemannian Geometry). Presenting my work at this conference, I received many good feedback that helped in designing my future research program. Since the week long program organized by Karigiannis and Craig was bringing together a very diverse set of mathematicians, I also benefited from listening to talks outside my direct sphere of influence.

On a more pragmatic level, the setup at BIRS is very conducive to research. Having a terminal in my bedroom, I was able to research literature pertinent to what I heard during the day and to prepare for the next day. The proximity of nice nature, good food, a swimming pool and a gym made my stay even more enjoyable.

In the long run, I would recommend that BIRS get equipped with a bigger research library.

I look forward to my next participation to a program at BIRS.

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David Rappaport, Professor, School of Computing, Queen's University

My first encounter with BIRS was in the summer of 2005 at the Bridges Renaissance Banff conference. I am a theoretical computer scientist and the Bridges Conference was my first encounter of the interdisciplinary world of the Bridges conference, which “bridges” the creative arts, education and mathematics.

My second trip to BIRS was for a stimulating workshop organized by George Hart and Reza Sarhangi ``Innovations in Mathematics Education via the Arts” (MathEd) that was held in the winter of 2007. At this workshop I met with Susan Gerofsky a specialist in Curriculum & Pedagogy from UBC. This summer at Bridges Renaissance Banff II, we have a paper that represents a collaboration with Susan, and two other colleagues of mine who were also at the MathEd workshop, Godfried Toussaint and Paco Gómez. Our paper explores the use of music and rhythm to provide visual, tactile, and audible stimuli when teaching concepts in mathematics.

The opportunity to attend meetings such as Bridges and the MathEd workshop in a setting such as BIRS is a treasure. The facilities at BIRS are first rate, and the setting in the mountains provides a truly wonderful environment in which to both relax and work hard.

Citations:

Francisco Gómez, Andrew Melvin, David Rappaport, and Godfried Toussaint Mathematical Measures of Syncopation BRIDGES: Mathematical Connections in Art, Music, and Science Banff, Alberta July 31 - August 3 2005 pp. 73-84.

David Rappaport Geometry and Harmony BRIDGES: Mathematical Connections in Art, Music, and Science Banff, Alberta July 31 - August 3 2005 pp. 67-72.

Susan Gerofsky Francisco Gómez, David Rappaport, and Godfried Toussaint Spirograph patterns and circular representations representations of rhythm: Exploring number theory concepts through visual, tangible and audible representations BRIDGES: Mathematical Connections in Art, Music, and Science Banff, Alberta July 26 - 29 2009.

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Anders Carlsson, Professor, Department of Physics, Washington University, St. Louis

This note is to express my appreciation for being able to participate in the ``Mathematical Biology of the Cell: Cytoskeleton and Motility" BIRS Workshop, held July 16-21, 2005. This workshop was very helpful to my research and professional development. The style of the workshop was such that it was very easy to meet people, and I got to know the research of several luminaries in the field as a result of my attendance. In fact, that workshop was the origin of a scientific collaboration that I have developed with the Max Planck Institute for the Physics of Complex Systems, in Dresden, Germany. This led to a five-month sabbatical visit which would not have happened otherwise.

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William Barlow, Research Professor, Department of Biostatistics, University of Washington

I attended a cancer risk prediction workshop this last winter at BIRS. It was a beautiful location and a terrific workshop. I was able to mingle with luminaries in the field of cancer risk prediction in an intimate setting. It was highly productive and we expect to publish a paper from the discussions. I very much support your application for continued funding of BIRS.

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Frithjof Lutscher, Associate Professor, Department of Biomathematics, University of Tubingen

I have been to BIRS on several occasions (five-day workshops, two-day short events) as well as in different positions (as a postdoc, as a young faculty member, and as a co-organizer). Each time the visit was very inspiring, very well organized, and highly productive. While I cannot point directly to a publication that arose from discussions at BIRS, each of these events has been crucial to my work and career. In particular at the beginning of my career, it was exciting to meet many experienced and internationally known researchers. I received invitations to visit and even to apply for a position. I also benefited from these meetings by reconnecting with researchers whom I had known and collaborated with before. I am still using the final report of one meeting as inspiration for new research projects. The environment (Banff, the Centre, logistics) and the friendly and professional staff make every stay there very comfortable. Their support to the organizers is amazing.

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Troy Day, Researcher, Department of Mathematics and Statistics, Queen's University

I have been involved with a couple of summer schools that have been hosted by BIRS in the area of Mathematical Epidemiology and Evolutionary Biology. These programs have been enormously beneficial, both to the instructors of the summer schools, and to the students. These summer schools attract people from all over the world and provide an unparalleled environment that is very conducive to intensive study. I have heard from many of the participants that these summer schools provided them with some of the best educational experience in their careers. It is a testament to the success of BIRS that these schools have been very much oversubscribed.

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Gordon Williams, Assistant Professor, Department of Mathematics, University of Alaska Fairbanks

I attended the session CONVEX AND ABSTRACT POLYTOPES from Thursday, May 19, 2005 to Saturday, May, 21, 2005. The conference was a pivotal one for me because through it I began a collaboration with Michael Hartley – an Australian mathematician I probably would not have met otherwise – that has resulted in one paper to appear in the Journal of Discrete Mathematics, and is likely to result in more publications. The questions and ideas that I became interested in through this collaboration now form the basis of my research program and the community of researchers I met with during the conference at BIRS continue to be influential in my work.

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Sven Gnutzmann, Professor, School of Mathematical Sciences, University of Nottingham

I have been at the Banff International Research Station for one week in February 2008 for the workshop `Quantum Chaos: Routes to RMT and beyond'. This has been an extraordinarily nice and successful conference which brought together physicists and Mathematicians from both sides of the Atlantic. The atmosphere at BIRS can only be described as marvellous - everything has been arranged to promote discussion and free thought. Scientifically I gained most from meeting a number of Mathematicians working in Northern America who I rarely meet at European conferences. Direct discussion among leading figures and younger scientists in the field is one of the most important and fruitful ways to advance science and the Banff International Research Station is one of the best places which promote workshops and small conferences which are ideal places for such discussions.

As a scientist I strongly support the new proposal to run similar workshops in all areas of mathematics at BIRS during the next 5 years.

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Finnur Larusson, Associate Professor of Pure Mathematics, Department of Mathematics, University of Adelaide, Australia

I am pleased to write in support of BIRS's proposal for continued funding of its operations. I have attended four workshops at BIRS since its founding. The most recent one, in June 2009, was on complex analysis and complex geometry. The group of participants was exceptionally strong. I found it an excellent opportunity to find out about the latest developments in the field, including some real breakthroughs, from the discoverers themselves, and discuss my own research problems with experts.

To give a few examples, I had discussions with Dr Frank Kutzschebauch from Switzerland on a new joint research project. Dr Jorg Winkelmann of Germany, a leading expert on group actions in complex geometry, was there, so I used the opportunity to ask him a number of questions related to my research. I had discussions with Dr Laszlo Lempert of the US about other research problems of mine, and he came up with a very elegant solution to one of them.

The facilities at the Banff Centre are excellent. The BIRS staff couldn't do a better job of facilitating research and communication for workshop participants. This, along with the spectacular natural setting, gives BIRS a real edge in attracting leading mathematicians, who typically get more invitations than they can accept.

BIRS is the only operation of its kind in North America and one of only a few in the world. It is a true asset to the world mathematics community. I very much hope that it will be able to continue.

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Ghassan AlRegib, Associate Professor, School of Electrical and Computer Engineering, Georgia Institute of Technology

I have been participating in various technical workshops and conferences and by far the BIRS Workshop on Multimedia, Machine Learning, and Mathematics II is the best technical workshop I have been to for the following reasons:

1. The workshop was well organized. 2. The technical talks and program were wonderful as it covered various topics that are educational to some participants and at the same time stimulated in-depth discussions by some other participants. 3. The chemistry and the ambiance the organizers created was wonderful. The ambiance allowed participants to freely share their ideas and technical views within a friendly environment over breakfast, lunch, dinner, social activities, and of course, during the technical discussions. 4. The participants were well picked to present various technical expertise and various research institutes and labs. Those were leaders in their fields. 5. The Banff Center was wonderful in its accommodation, meal services, and the various help the staff provided. Simply wonderful. 6. The fact that the workshop was in Banff is brilliant and enough said about this pick as BIRS's home.

I finally thank BIRS, the workshop organizers, the Banff Center staff, and all those who contributed to make this happen.

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Byron Roe, Emeritus Professor, Department of Physics, University of Michigan

I attended the 2006 BIRS conference on statistics in physics (and chaired a session). This conference looked at current statistical problems in particle physics and astrophysics. It was one of a series of conferences that we have had in recent years studying the statistical problems in these disciplines.

This set of conferences has remarkably improved the level of statistical sophistication for those of us in physics over the last few years, and, I believe, has been valuable for our mathematics colleagues by introducing them to the many and special statistical problems in our disciplines.

I found the BIRS conference to be extremely valuable. For upcoming experiments at the huge CERN accelerator we are striving to set limits on the existence of new particles and processes at a probability level of what would be five standard deviations for a normal distribution. A considerable amount of information was gathered during the meeting, and, over the next year, a number of important publications appeared which looked at various recipes and attempted to demonstrate how well they worked for a number of situations using Monte Carlo generated data. These investigations will be crucial once the CERN machine starts taking data later this year.

In addition, a number of strategies were examined for data mining, and, again, there was a large amount of discussion of these methods after the meeting. A competition was set up at the meeting to examine various methods of separating small signals from data and this competition also continued for a considerable time afterwards.

The location and surroundings of your venue were superb and contributed strongly to the pleasure we had at the meetings and to the enthusiasm of the participants. I strongly support the continuing support of scientific workshops at the Banff International Research Station and hope we can have another statistics in physics and astrophysics workshop there in the future.

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Nancy Reid, Professor, Department of Statistics, University of Toronto

I helped to organize, and participated in, a five-day workshop in July 2006 on ``Statistical inference Problems in High Energy Physics and Astronomy". The high energy physics community has a series of ``Phystat" workshops on statistical issues in HEP, but this BIRS workshop gathered a much larger group of statisticians, approximately 1/2 the attendees, to be exposed to and to participate in solving statistical problems for HEP and astronomy, with particular emphasis on problems related to experiments at the Large Hadron Collider at CERN. My participation in this workshop led directly to my participation at Phystat 07, where I gave an invited paper on design of experiments, published in the proceedings of that meeting. The workshop also led to what came to be called ``The Banff challenge", see http://newton.hep.upenn.edu/ heinrich/birs/ designed to find the most reliable and efficient statistical method for use in the problem of establishing discoveries from noisy Poisson signals.

This workshop was personally very rewarding and exciting, and led to ongoing collaborations in high energy physics. I was also very pleased to be able to encourage a larger group of statisticians to work in this field; the contribution of Davison and Sartori (http://infoscience.epfl.ch/record/125046/ files/physics7.pdf) to the Banff challenge is especially noteworthy, as it appeared in Statistical Science, one of the most prestigious and widely read statistics journals.

BIRS is a wonderful resource for science and for Canada and I support it in the strongest possible terms.

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Michael Falk, Professor, Department of Mathematics and Statistics, Northern Arizona University

I was a participant in two FRG's, in June, 2005 and June, 2006, on subjects related to hyperplane arrangements. It was a wonderful working. Much of the work on an impactful joint paper with Sergey Yuzvinsky was done at Banff. That paper was published in Compositio math.:

``Multinets, resonance varieties, and pencils of plane curves, with S. Yuzvinsky, Compositio mathematica, 143 No. 4 (Steenbrink issue) (2007), 1069-1088."

Also at that 2005 FRG we worked out a lot of the issues surrounding the comprehensive book on complex hyperplane arrangements that the seven participants are writing. That book is close to being finished.

At the 2006 FRG I worked closely with Dan Cohen and Graham Denham on a joint project which resulted in two papers, on resonance varieties and critical loci of master functions (Alexander Varchenko is the fourth author). One of those papers has been completed and is currently under review at the Canadian Journal of Mathematics.

BIRS is a great place to do mathematics.

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Agata Smoktunowicz, Professor, School of Mathematics, University of Edinburgh

I attended the meeting on Noncommutative algebraic geometry 26-30 October 2008.

It was a great meeting and I enjoyed it very much.

I met a lot of scientists in my area who I had never meet before (only from publications and not personally) and also talked with my friends and collaborators. I also had many very stimulating and interesting research conversations. It was a marvellous meeting in every way and in a very beautifull place.

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Agelos Georgakopoulos, Researcher, Institute of Mathematics, Technical University of Graz

I participated in a 1-week workshop on infinite graphs in October 2007. This was a very valuable professional experience. In BIRS I was able to meet, for the first time, many researchers working in areas related to mine, and had the opportunity to present my work to them and hear about theirs. One of the contacts I made there flourished into a prolonged research visit, which gave rise to one of the research problems I'm still working on.

The BIRS station provides excellent facilities for carrying out such meetings, and is situated in a stimulating environment. Compared to other conferences, it has the significant advantage that the participants are accomodated close to the lecture and free-time facilities, which gives us the opportunity to continue our scientific discussions after the end of the last talk of the day.

Thank you for giving me the opportunity to attend one of your meetings!

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John P. D'Angelo. Professor, Department of Mathematics, University of Illinois at Urbana-Champaign

I was a co-organizer and participant in the meeting on Analytic and Algebraic Methods in Complex and CR Geometry held September 4-8, 2005.

This meeting was excellent, and I praise the staff at BIRS for their efforts.

1) The scientific quality was high. 2) The collegiality and opportunities to converse were excellent. 3) The setting is idyllic. 4) The staff made it work. 5) It was easy to get there, and the accomodations were great.

I have attended and/or co-organized many meetings in my career. I felt that that meeting was among the top 5-10 percent of all those meetings.

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Norman Dancer, Professor, School of Mathematics and Statistics, University of Sydney

I have found my visits to the centre immensely rewarding. I have learnt of new work (which is very important for me since I live in a place some distance from the main centers of mathematics). The centre makes it easier to develop collaborations, because it is easier to meet informally. In particular, this has benefited collaborations of mine with Hilhorst and Wei (these have become papers). Moreover,I have had very valuable discussions which have not lead to papers but changed my entire research program.In particular, I am thinking of discussions with C.Gui.

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Arnaud Beauville, Professor Emeritus, J.-A Dieudonne Laboratory, University of Nice

Let me point out the paper

arXiv:0902.3721 Title: On the Brauer group of Enriques surfaces Author: Arnaud Beauville

which is an outcome of a problem session during BIRS Workshop 08w5083 Arithmetic of K3 surfaces

I confirm. The paper is accepted in Math. Research Letters.

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Karlheinz Groechenig, Researcher, Department of Mathematics, University of Vienna

Since 2005 I have attended three BIRS workshops and co-organized one of these. I love to visit BIRS. It is superbly located and easily accessible, even from Europe. The atmosphere is absolutely wonderful and inspiring.

Workshops at BIRS help me to meet my collaborators and continue our work. In a long-term collaboration the personal contact is absolutely important. I have made new contacts at BIRS: a workshop at BIRS helps me both to meet my mathematical family and to get to know the important new researchers in my field.

One of the workshops I attended (Organizers: Jorgensen, Larson, Kribs, etc.) united mathematicians from several different fields and exposed me to completely new ideas and points of view. Since then I have taken a deeper interest in certain aspects of operator algebras and produced several papers in this direction.

In a time of increasing speed and busyness, research stations like BIRS (or Oberwolfach or the Erwin Schroedinger Institute or the MSRI) have an indispensable role. BIRS is like an oasis. It offers perfect conditions for research and for interaction. BIRS offers an environment where creativity is still possible and stimulated. Everyday academic life is too full of chores and things-to-do, all of which rather stifle creativity.

I strongly support the renewal and increase of funding for BIRS.

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Andy Wathen, Reader in Numerical Analysis Tutorial Fellow, Computing Laboratory, Oxford University

BIRS is indeed an excellent thing, providing a special research environment for Mathematicians from around the World. My experience is of a truely international event in Banff where almost all of the best researchers in the World in the specific subject of our Workshop were pleased to be invited and did attend.

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Congming Li, Professor, Department of Applied Mathematics, University of Colorado

I have been a visitor at MSRI, IAS, and BIRS and I like the BIRS the best!

It gives you a chance to listen to some talks about new development yet not too many! This subtle balance is the most important character of BIRS.

With this balance, we can have time to engage in private discussions and to find collaborators for future research.

The hiking environments also help us to build friendships amongst ourselves and to make the stay more relaxed.

The week long workshop seems to be the right length.

I love BIRS.

Long Live BIRS!!!!!!!!!!!!!!!!!!!!!!!!

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Peter Smereka, Professor, Department of Mathematics, University of Michigan

The Banff International Research Station has become a vital resource for the mathematics and scientific community. I have had the pleasure to visit BIRS on three occasions: twice as a participant in a 5 day workshop and once as an organizer of one. In each case, the workshops were incredibly successful and I am planning to submit a proposal this fall to organize another five day workshop.

In my mind, there three reasons BIRS workshops are so successful. First, the size is limited to about 40 people which is really a perfect number for a highly focused meeting. Second, the environment is ideal: an attractive and isolated setting allowing the participants more opportunity for interaction. Third, the staff is amazing: everything runs smoothly and the meetings proceed without any problems.

Its continued support will be of great benefit to mathematicians and scientists worldwide.

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Morten Hegner Nielsen, Assistant Professor, Department of Mathematics and Statistics, University of Winnipeg

I visited BIRS for the week of August 3-9, 2008, to participate in the focused workshop ``Traceability of Graphs and Digraphs" along with some colleagues from my department; one from the USA, and two from South Africa. Given our geographical separation it is clear that we rarely get a chance to meet for collaborative work. Also, whenever workshops are held in a private setting, invariably much time and energy goes towards practical issues such as grocery shopping, cooking, cleaning etc. Yet another limiting issue - depending on participants' personal research grants (as a beginning researcher I do not yet have one) - is the expenses derived from accommodation.

These facts in themselves make an option such as that provided by BIRS highly welcome and valuable to any researchers who wish to arrange a workshop. I must say I was very impressed indeed by the BIRS facilities, service, and concept as a whole. One can hardly image a better setting: Participants are provided with the infrastructure necessary for such a workshop as well as meals - which, by the way, are all exquisite - and no time is wasted on irrelevant practical matters. The added benefit of the stunning beauty and scenery of the Canadian Rockies obviously helps make the event an even more rewarding experience. In fact, I strongly believe this aspect positively affects creativity by providing a pleasant, inspiring, quiet, and healthy environment. There really is nothing quite like a stroll in the mountains after a delicious lunch, before returning to work.

The fact that this workshop yielded two research papers in one week (both of which were submitted shortly after the meeting) should serve as evidence that providing the research community with an opportunity such as a BIRS workshop most certainly is worthwhile.

In every way that week in Banff was very giving, and I strongly recommend the further support for BIRS.

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Mike Boyle, Professor and Chair of the Undergraduate Program, Department of Mathematics, University of Maryland

After wanting but not being able to participate in some past Banff conferences, I participated in the hidden Markov chains conference organized by Marcus et al.

I was very pleased with the conference itself. It also led to my collaboration with Karl Petersen on a 50+ page, mostly expository paper on various approaches to hidden Markov chains. There is a good chance that this will be of nontrivial value, and in the process I've come to a better understanding myself of various results and questions. I also communicated with some experts outside my acquaintance I would not otherwise have met or contacted. One answered a question I'd wondered about for over 20 years.

Definitely this conference had considerably more impact on me than the usual conference.

A really wonderful feature of the conference site is the design of the dining area, which provides an absolutely stunning view of the beautiful surroundings.

I look forward to returning when I can.

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Barbara Fantechi, Professor, Mathematical Physics Sector, SISSA

It is a great pleasure for me to be allowed to express my opinion about BIRS. I will not go into big detail, since I am currently on sick leave; however, since my leave will terminate in September, I've decided it is better to send a timely report than a polished but late one.

I was at BIRS only once last March. It was a conference featuring a very focused program, and involving a mixture of young and experienced mathematicians. I learned a lot, and gained new perspectives that have shapen my subsequent research. I also started a joint research project (which I have now put on hold due to sickness).

My PhD student also took part in the event; his talk was very well received, and gave him the opportunity to get in touch with a number of experts in the field. He is going to graduate in August and he will then start a two-year postdoctoral position with a mentor he met at BIRS. Another BIRS participant will act as external referee; I asked him since he was interested in the result.

I also got occasion to talking with other graduate students there and I was told talking to me had been helpful.

A very good thing is that everybody shares the same facilities, which makes this type of conferences decidedly superior to those where participants are scattered in a number of hotels in some town and end up seeing each other only during talks, and otherwise hanging around with those they already know.

I think I needn't say much about the beauty of the location and the quality of food and accomodation; everything is excellent.

Of all the conference locations I have experienced, I would compare BIRS with only two in the world, namely CIRM in Luminy (near Marseille, France) and Oberwolfach (mfo.de), with Oberwolfach having an edge since it also has a mathematical library. However, year by year this advantage dwindles, as more and more papers and books become available in electronic format.

The only thing I really dislike about BIRS is how far away it is from Europe, but I guess this is actually a feature for all Americans who have a symmetrical complaint about Oberwolfach.

Please keep funding this awesome venue, which as far as I know is one-of-a-kind in the North American continent.

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Weiqiang Wang, Professor, Department of Mathematics, University of Virginia

I have been to BIRS for multiple of times, the latest one being in May 2007. I always found the meetings at BIRS scientifically very stimulating. Of course, the location of Banff contributes also greatly to the quality of the social and scientific life. I personally regard it as one of the few places where I want to get back as often as I can (another of my favorite is MSRI, Berkeley; I will compare BIRS favorably to IAS, MPI, Oberwolfach, RIMS).

For example, during the 2007 workshop, I received a crucial information through an informal discussion with another expert, which helped me (and my Ph.D. student) to overcome a difficulty which we got stuck for over one year. As results, we have been able to complete two papers since then, one appeared in Proc. LMS 2009, and another submitted to J. Algebra.

It is my sincere hope and belief that BIRS will continue to run in the future as successfully as it has been. It has been an invaluable service to the international math community.

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Narutaka Ozawa, Associate Professor, Graduate School of Mathematical Sciences, University of Tokyo

First of all, thank you very much for keeping to provide a nice environment for math conferences. I'm an operator algebraist who had participated in 08w5093 Topics in Von Neumann Algebras. There, I had a fruitful conversation with Prof. Tornquist, a logician, and was able to solve a certain problem which was in my mind for a few years. I've written a paper on this and acknowledged at the end of introduction. http://arxiv.org/abs/0804.0288

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Gitta Kutyniok, Professor, Institute of Mathematics, University Osnabrueck

I attended several workshops at BIRS over the last years as well as organized one by my own. Each time I significantly benefitted from my visits due to the professionality with which the staff at BIRS is organizing these events. The facilities are excellently managed, and the information and support which participants as well as organizers receive is superb. Hence as a researcher you can concentrate entirely on the scientific exchange with your colleagues. In my case this often led to new collabo- rations, where joint work already started at BIRS during evening hours in the very nicely arranged common room. Also the rooms, where talks take place, are to my mind - and everyone I spoke to of my colleagues - perfectly equipped both from a techological viewpoint as well as from a psychological one. Henceforth I consider BIRS a mathematical facility which is crucial for scientific progress. Therefore, summarizing, I strongly support BIRS in any aspect.

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Christian Robert, Professor of Applied Mathematics, Universite Paris Dauphine

As both a participant and the co-organiser of one meeting at BIRS, I want to testify my strong support for the continuation of its activity in the coming years. The unique appeal of BIRS for North American meetings is to provide a secluded spot with facilities of the highest quality to conduct workshops with no side perturbations. As an organiser, I was particularly pleased with the fact that I had nothing to do but attend and participate to the talks and discussions once the meeting had started. As a participant, I deeply appreciated the possibility to concentrate on the meeting and to use the campus facilities to refresh my concentration. The quality of the accomodation is exceptionnal.

At the scientific level, I think this meeting was the second to best workshop I attended over the past 5 years. In particular, the quality of attention and attendance from the audience of invited participants was at its highest degree, in that everyone attended every talk (except for one unlucky participant who got sick early on) and that discussions had to be stopped for the next talk to start! The BIRS meeting also immensely helped me to make progress on the specific topic of ABC algorithms, topic of which I have now written three papers and completed the advisal of one PhD student. In addition, the work on noninformative Bayesian model choice we presented during the meeting induced two other groups of researchers to pursue research on the same topic.

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David V. Cruz-Uribe, SFO, Professor, Department of Mathematics, Trinity College Hartord

I was a co-organizer of a conference at BIRS in the spring of 2008. I found the entire experience really wonderful. We were able to get a very strong group of researchers to come to the meeting, and during the free time I was able to have a number of informal discussions with them which contributed significantly to my work. In particular, my co-author Cristian Rios and I were able to make good progress on our work on the Kato problem for degenerate elliptic operators, and we expect to complete a paper later this year based on ideas that came directly from this conference.

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Ty Ferre, Associate Professor, Department of Hydrology and Water Resources, University of Arizona

Simply stated, I have never been to a conference center that is better run than BIRS. The setting is perfect - both promoting intensive scientific interaction and providing recreational activities to let off steam. The food, housing, and meeting rooms were perfect, as well. In our case, BIRS allowed us to bring together scientists from three continents to help to define the critical next steps for the advancement of hydrogeophysics. Participants had backgrounds in geophysics, hydrology, and mathematics. As such, it is unlikely that they would have come together through any other venue. The most tangible outcome was the publication of a Forum article in EOS, the most widely read publication in earth sciences. But, the more lasting impact will be the contacts that were made and reinforced during our meeting in Banff. In summary, BIRS is an invaluable resource that is highly deserving of support.

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Ted Chinburg, Researcher, Department of Mathematics, University of Pennsylvania

I'm writing concerning my experiences working at BIRS on the Research In Teams project 08rit135, ``Finiteness problems in arithmetic deformation theory," from July 27 to August 3, 2008.

I worked on this project with Prof. Frauke Bleher of the University of Iowa. It was exceptionally useful to have a solid week to work on this at BIRS. The facilities were perfect for this purpose, In particular, it was quite helpful to have whiteboards in two rooms to work through various calculations. On the last day of the project we were able to finally straighten out an intricate spectral sequence calculation which had been a stumbling block for months. This led to being able to complete the following preprint by the end of 2008: http://arxiv.org/abs/0901.0101 This preprint has been submitted for publication, and in the published version of it we will thank BIRS for supporting this research.

I do think that the Research in Teams program at BIRS provides a unique opportunity for small groups of mathematicians to make focused, rapid progress on hard research problems. I wish that there were more organizations in North America supporting mathematical research in this way! BIRS is a unique institution.

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Wilfried Sieg, Patrick Suppes Professor of Philosophy & Mathematical Logic, Department of Philosophy, Carnegie Mellon University

I participated in a highly interdisciplinary workshop. It was intellectually stimulating and enriching; of course, that can be said of many workshops and conferences. However, Banff was special: the supportive environment of BIRS and the intensity of interaction contributed immensely to the success of the workshop I attended. In my case it did not lead directly to collaboration after the workshop, but it inspired me to reshape significantly the paper on which my contribution had been based.

I hope for BIRS's continued success!

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Detlev Hoffmann, Professor, Division of Pure Mathematics, School of Mathematical Sciences, University of Nottingham

Here are a few of my impressions about BIRS:

BIRS is one of only a handful of comparable institutes worldwide that covers the WHOLE range of mathematical endeavour in week-long workshops and similar activities year-round. Being myself an organiser of workshops at Oberwolfach in Germany (another one of these handful of institutes), I can testify that a place like BIRS satisfies an essential need of the mathematical community, bringing together the foremost established experts as well as promising young talent to present and discuss the latest advances in a particular mathematical topic in an environment conducive to fruitful and productive interaction. Having attended workshops in BIRS, I can confirm that each time this has been a wonderful experience with regard to the high quality of the mathematics that has been presented as well as with respect to the social interaction with other experts in my and related fields. It is especially this latter aspect which has impacted my own research because through this social interaction, one quickly develops an interest in other people's research from which one draws inspiration and ideas for one's own research.

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Robert Griffiths, Professor, Department of Mathematical Genetics, University of Oxford

I attended the workshop Stochastic processes in ``Stochastic Processes in Evolutionary and disease Genetics" August 8-12 2004 at BIRS. This was my 2nd workshop at BIRS. It was an excellent workshop with cutting edge research talks and an opportunity to discuss research problems with participants which I made the most of. There were researchers with international home locations from USA, Canada, Europe and UK. The location, facilities and conference arrangements were excellent. I am attending and speaking at a BIRS workshop ``New mathematical challenges from molecular biology and genetics from 6 Sept - 11 Sept this year, 2009.

BIRS is a valuable mathematics research center and deserves continued funding.

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Mattias Jonsson, Professor, Department of Mathematics, University of Michigan

I participated in the workshop ``Multivariable Complex Dynamics" from March 1 to March 6, 2009. It was an excellent experience. Not only were the lectures great, but BIRS provided an intimate atmosphere which facilitated informal discussions that greatly enhanced my understanding of several topics in the [research] I am working on. It was also extremely fruitful for my graduate student, who I brought along.

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Francesco Chiacchio, Researcher, Department of Mathematics, University of Naples Frederico II

I attended the BIRS Workshop on ``Geometric Inequalities" (June 17-22, 2007). The meeting gave me the opportunity to interact, in a friendly atmosphere, with leading experts in optimal transportation, rearrangements, geometric flows and spectral geometry. The discussions were informal but very deep and many suggestions for future research have emerged. Finally, I found the conference location absolutely stunning.

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Deli Li, Professor, Department of Mathematical Sciences, Lakehead University

The ``09w5004: Advances in Stochastic Inequalities and their Applications" workshop at BIRS was well organized so that it was very successful. During the workshop I enjoyed the talks presented by so many distinguished researchers. Because of the workshop, I have done a research paper recently.

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Pierre McKenzie, Professor, Department of Computer Science and Operational Research, University of Montreal

In case this can add to the BIRS case, part of the work leading to the paper below, specifically between the co-authors Braverman and McKenzie, was done at BIRS:

Pebbles and Branching Programs for Tree Evaluation, Mark Braverman, Stephen Cook, Pierre McKenzie, Rahul Santhanam, Dustin Wehr. Draft manuscript, 45 pages. (Part of this will appear in MFCS 2009.)

The preprint of the paper can be found at http://www.cs.toronto.edu/ sacook/#publications

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Irena Swanson, Professor, Department of Mathematics, Reed College

I was in Banff in the spring of 2007, I believe. What was great that at the time I was in the middle of trying to understand some primary decomposition and integral closure questions, and it was great that Holger Brenner, Paul Monsky, Anurag Singh, Shunsuke Takagi, and Tony Geramita were present. We had some interactions that were very useful to me. No papers or big discoveries were made then, and Brenner and I tried to work a few things out for a few months afterwards, but that particular project did not work out. Nevertheless, I learned a lot. Without Banff, I wouldn 't have talked to Brenner, Monsky, Takagi, or Geramita.

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Robert Platt, Associate Professor, Department of Epidemiolog and Biostatistics, Department of Pediatrics

I recently participated in the workshop ``Causal Inference in the Quantitative Sciences" held May 3-8 at BIRS. I served as one of the on-site organizers of the session with Jay Kaufman and Tyler VanderWeele (in place of the organizers, Erica Moodie and David Stephens, who were unable to attend for personal reasons).

The workshop was excellent. I was able to continue collaborations with colleagues who also attended the session, and had numerous opportunities to discuss research and research projects with a wide range of people. This group was from a range of research areas, and it is extremely unlikely that I would have had exposure to such a group in another setting. I also used results from presentations at the BIRS workshop to further my own work; the presentations by Hernan and Robins led directly to improvements in research projects that are ongoing in my group. Finally, the McGill attendees of the workshop have now formed an interdisciplinary reading group in causal inference (including statisticians, economists, computer scientists, and epidemiologists); this latter group would not have formed if not for the workshop.

On another note - the organization and resources of BIRS were top-notch. The workshop went smoothly on all axes, and without any problems. The services and support from BIRS and the Banff Centre were great. I would not hesitate to attend other workshops at BIRS.

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Domenico Marinucci, Chairman, Department of Mathematics, University of Rome Tor Vergata

I was in Banff in February 2009 for the meeting on stochastic geometry organized by Proff. Adler, Taylor and Worsley.

Most likely, it has been one of the most (if not THE most) useful meetings of my academic life (I am 40 and I have already attended dozens). The audience was exceptionally well-qualified, and it was a unique blend of people addressing close issues from very different perspectives, or using the same tools for very different purposes. Researches ranged from pure geometry to medical statistics, from mathematical physics to image analysis and several other topics. I had the opportunity to come across several people whom, I discovered, were doing things related to mine, although in a completely different environment. Just to give a few examples, let me tell you I work on the harmonic analysis for spherical random fields, with a view to applications in cosmology (especially Cosmic Microwave Background radiation). At the meeting I met Igor Wigman, who started as a number theorists and he is now involved in random eigenfunctions of spherical laplacians - it turned out these can be viewed as geometric functionals of the high frequency Fourier components of a spherical random field, and we started a collaboration about that (this is just at the beginning, but looks promising - he will come to visit me in Rome after the summer). I also got acquainted with Mark Dennis (Bristol), who works on quantum optics, but again he has results on the zero of random polynomials (the Majorana approach) which could be very useful for what I am trying to do. Just this week, I wrote to Armin Schwartzman (Harvard), who presented results on brain medical imaging: he studies fields which take tensor values, and this is in perfect analogy with what I am doing (with Daryl Geller and Xiaohong Lan, which were not there) on spin random fields for polarization data analysis in CMB. Also, one week ago I got a few emails from Kevin Bartz, a student from Harvard who was at the conference and is now trying to apply results from random geometry to non-Gaussianity in CMB radiation, so he contacted me for some advice. I could provide more examples, but I think this is enough to prove the workshop was incredibly successful.

In short, many thanks again for your hospitality - I do hope to be able to come back.

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Benjamin Doerr, Researcher, Department 1: Algorithms and Complexity, Max-Planck Institute of Technology

I would gladly share my experience at BIRS. I was invited to participate a 5-day workshop on ``Coarsely Quantized Representations of Signals in March 2006. I'm working in discrete mathematics, so I was surprised to be invited to a workshop on signal processing.

At the workshop, I learned that there is a strong connection between discrepancy theory and rounding problems (one of my research areas) and quantization problems in signal processing. I had never thought of this, and without the workshop, I would most likely never have seen this connection. I should say that the discrete mathematics and the signal processing communities naturally do not share many interests, and therefore, are quite disjoint.

In addition to this valuable insight, I found that Sinan Gunturk (in fact one of the organizers of the workshop) was working on a problem closely related to a previous work of mine. With joint forces, we made significant progress. Prof. Gunturk visited me at the Max-Planck-Institute (Saarbruecken, Germany) in 2007 and we continued working on this problem. We should be able to publish the results soon.

In summary, the workshop gave me insight into a completely different field and started a crossdisciplinary collaboration that otherwise would have never begun. The organizers both of the workshop and of the station in general did an excellent job. I'm looking forward to returning to Banff. I would rate Banff in one league with the established centers of Oberwolfach and Dagstuhl (more computer science, but also hosts mathematical topics with possible connections to CS).

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Carol Bier, Islamic Art Historian, Research Associate, The Textile Museum, Washington DC

[This year] will be my third visit to Banff and BIRS, the others also associated with Bridges, and the Mathemetics Innovations in the Arts research residency.

I wanted to share some of the rich results of my earlier experiences with BIRS projects: 1) an article (``CarpetMath: Exploring Mathematical Aspects of Turkmen Carpets") soon to be published in the Journal of Mathematics and the Arts, in a special issue devoted to art in mathematics education (September 2009), which emerged directly from our BIRS workshop and is being edited by Mara Alagic, who was also one of the participants, 2) further collegial exchanges in particular with two other participants from that workshop, Pete Wells and Phil Wagoner, who have contributed to the present Bridges proceedings; 3) inquiries into the prospects for a Board meeting of the Textile Society of America, and for a biennial conference of TSA at Banff International Center, whose conference facilities are indeed outstanding and would serve us well (I am immediate past president of TSA); 4) plans to submit a proposal to BIRS for a five day workshop addressing ``Perspectives on Geometry in Islamic Art," for which both mathematicians and Islamic art historians would be invited to participate as presenters.

All the best, and with great anticipation of Renaissance Banff II.

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Zinovy Reichtstein, Professor, Department of Mathematics, University of British Columbia

Since 2003 I have coorganized three BIRS workshops and attended several others as a participant. These workshops have had a major impact on my work. I have made numerous professional connections [at BIRS] and learned a great deal of mathematics from other participants, in the lecture hall, in the dining room and on the hiking trails. Several of my most significant recent papers have been conceived there, and many others have been shaped, influenced or improved as a result of these interactions. I invariably return from Banff energized, with several new ideas and projects and sometimes with new collaborators.

BIRS is an important resource for the mathematical community all over the world; mathematicians talk about it everywhere I go. I feel fortunate to have it so close to home.

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Javad Tavakoli, Associate Professor, Department of Mathematics, University of British Columbia, Okanagan

A Productive Time at Banff due to BIRS:? In 2006, we had a very productive meeting of Canadian Queueing Systems Conference (CanQueue), the yearly meeting of people in queueing theory in Canada. This meeting was attended by many specialists and graduate students around Canada in queueing theory, and we had a very interesting program. The keynote speaker was Carey Williamson from the University of Calgary, who talked about priority systems in computer applications. During two days of the meeting, it was a great opportunity for me to meet my colleagues from different universities and discuss some of issues related to my research interest in queueing systems for which I have received a number of useful references. I am sure others made similar acquaintances, and that their research profited in this fashion. In conclusion, I believe that having the opportunity to join others to discuss problems of common interest is absolutely essential, and Banff is an ideal place for this. For this reason, I believe that BIRS can make a very valuable contribution in any area of mathematics, and must be fully funded.

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Michael E. Zieve, Researcher, Department of Mathematics, Rutgers Unviersity

I attended the BIRS workshop ``Polynomials over finite fields and applications", Nov 18-23 2006. There were several inspiring talks which introduced me to topics I intend to look into when I find time. Of particular importance to me was meeting Ariane Masuda and seeing her talk, which contained two interesting conjectures. We discussed these at length, and resolved them in the joint paper ``Nonexistence of permutation binomials of certain shapes", Electronic Journal of Combinatorics 14 (2007), N12. We continued this work and obtained a very satisfactory description of permutation binomials over prime fields, vastly improving a series of previous results by many authors, in our paper ``Permutation binomials over finite fields", Transactions of the American Mathematical Society 361 (2009), 4169-4180. Since then we have worked on several joint projects, which will ultimately yield several papers; at present the only one of these which has appeared is ``Rational functions with linear relations", Proceedings of the American Mathematical Society 136 (2008), 1403-1408. My continuing collaboration with Ariane has been a rewarding outcome of this workshop.

Also at the workshop I was intrigued by the lecture by Steven Wang. He used unexpected tools to give complicated proofs of some interesting results. This led me to find simple and natural proofs of more general results, which appeared in my papers ``Some families of permutation polynomials over finite fields", International Journal of Number Theory 4 (2008), 851-–857 and ``On some permutation polynomials over GF(q) of the form $x^rh(x^{(q-1)/d}$)", Proceedings of the American Mathematical Society 137 (2009), 2209-2216.

In addition to this, I had several fascinating conversations with Hendrik Lenstra, in which we proved a number of results that will eventually be published.

All in all, this workshop was a stimulating experience with many long-term mathematical benefits for me.

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Raphael Gottardo, Assistant Professor, Department of Mathematics, University of British Columbia

I have been one of the organizer of a BIRS workshop on ``Bioinformatics, Genetics and Stochastic Computation: Bridging the Gap". As an academic scientist, I have been to many conferences and workshops across the world and I can easily say that BIRS provides one of the best environment in the world to hold a scientific workshop, by far. BIRS provides great facilities and services so that participants can simply focus on research. Banff is an ideal location for holding a workshop because it is secluded and once participants arrive in Banff, collaboration becomes very natural. In addition, the Canadian Rockies provide great opportunities for outdoor activities (e.g. group hikes) which can facilitate networking and informal discussion.

As a junior faculty member, our workshop has really helped me to jump start my career by giving me the opportunity to meet, discuss and present my research results to world class leaders in my field.

I thank you for running such great facilities and wish you and BIRS the very best of luck!

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Anthony Harkin, Director, Center for Applied & Computational Mathematics Rochester Institute of Technology

I attended the workshop on Dynamical Systems & Applications, June 22 - 24, 2007 organized by Mike Radin (Rochester Institute of Technology). This was simply one of the best mathematics workshops I have ever attended. It was extremely informative and the contacts I made at the workshop have been quite valuable. Specifically, I met Herb Kunze (University of Guelph) and Eric Bolt (Clarkson University), both of whom I invited to visit RIT after the BIRS workshop to help me promote RIT's new Center for Applied and Computational Mathematics (acm.rit.edu). In addition, one of the other contacts I met at BIRS, Alexandra Landsman (Naval Research Lab), we almost hired for a tenure-track position in our math dept.

I would eagerly attend a similar workshop at Banff in the future.

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Charles M. Newman, Professor, Department of Mathematics, New York University

Here are a few short comments (in the short time available).

I've attended two BIRS meetings, one in May/June 2005 and one in Nov. 2006 and will be attending another in Nov. 2009. The one in 2005 was particularly exciting as it was on the fairly hot topic of Critical Scaling for Polymers and Percolation and the participants included John Cardy, Greg Lawler, Yuval Peres, Stefan Rohde, Scott Sheffield and Wendelin Werner (soon to win a Fields medal for work including what he discussed at BIRS). Looking back at my notes from some of these talks (e.g. Werner's talk on loop soups and loup ensembles), I see a direct link between what I learned there and the recent work I've done and am doing with Federico Camia and Christophe Garban (who recently finished his PhD under Werner) about scaling limits of the two-dimensional Ising model in terms of measure ensembles. The first paper of this work (of Camia and me) was published in Proc. Nat. Acad. Sciences 106 (2009) 5457-5463.

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Radu Craiu, Associate Professor, Department of Statistics, University of Toronto

I have participated at one conference organized at BIRS in 2008. It was a fantastic experience! I enjoyed the great facilities, the presentation rooms and the scenic surroundings. The conference went smoothly, there were no ``glitches" and everybody was impressed by how well things fell into place. The opportunity to interact with my fellow researchers in such an environment is simply priceless. In particular, I have developed a new research direction (adaptive Markov chain Monte Carlo) as a result of the BIRS conference. Thank you!

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Vladimir Tonchev, Professor, Department of Mathematical Sciences, Michigan Technological University

I had the privilege to participate at the Workshop 09w5071, Invariants of Incidence Matrices, held March 29 - April 3, 2009.

I found the experience of attending the workshop invaluable. Its impact resulted in extending the results I presented at the workshop into new directions that lead to the following two papers that were written in the months following the workshop:

D. Clark, D. Jungnickel, and V.D. Tonchev, Affine geometry designs, polarities, and Hamada's conjecture, J. Combin. Theory, Ser. A, submitted on July 10, 2009.

A. Munemasa and V.D. Tonchev, The twisted Grassmann graph is the block graph of a design, Innovations in Incidence Geometry, submitted on July 13, 2009.

The BIRS workshops provide a unique creative atmosphere and opportunities for exchanging new ideas and emerging trends in the mathematical sciences. I hope that your efforts to secure funding for future activities are highly successful.

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Mirjana Vuletic, Department of Mathematics, Caltech University

I was a participant in one of the 5-day workshops organized at BIRS in 2008. It was an exceptional workshop. Our program consisted of talks, problem sessions and informal participant gatherings where we talked about our research. The atmosphere in the station and the way it is organized promotes interaction between participants which I find the most valuable. It is of great importance when in addition to someones talk you can share experiences in a more relaxed and informal way. BIRS provides such opportunity and I benefited from talking to other participants and believe that in the future I will collaborate with some of them. The station is located in a beautiful area that is very inspiring to work.

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Christine Lescop, Researcher, National Center for Scientific Research, University of Grenoble

I have been a participant at the [following] workshops: The Many Strands of the Braid Groups 07w5104, April 22 to April 27, 2007. Braid Groups and Applications 04w5526, October 16 to October 21, 2004.

These excellent workshops gave me the opportunity to meet mathematicians I had not met before, to learn a lot, and to share my own work in a very stimulating atmosphere.

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Jinqiao Duan, Professor, Department of Applied Mathematics, Director, Laboratory for Stochastics and Dynamics,Illinois Institute of Technology

In September 2008, I participated in the small workshop on stochastic dynamical systems driven by fractional Brownian motion. Being correlated in time, fractional Brownian motion provides an appropriate mathematical model for colored noises. (Most research on stochastic dynamical systems are for systems driven by white noise.) This workshop is a synchronized action which gathered a few top experts in this emerging research area, and inspired new ideas for further research and pointed out applications in biological and geophysical sciences. This workshop made me clear that this is a viable research area and new advances are imminent. I would like to participant more such workshops at Banff.

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Anne Vanhems, Professor of Econometrics, Toulouse Business School

I attended the workshop ``Semi and nonparametric methods in econometrics" in Banff last April 09, and greatly appreciated this meeting. It was focused on a mainstream area of econometrics with a lot of top researchers in this field. It was most interesting and useful for my research.

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Serban T. Belinschi, Assistant Professor, Department of Mathematics and Statistics University of Saskatchewan

My first participation in a BIRS programme has been in the fall of 2004, in my last year of PhD studies, at a Free probability 6-day workshop, organized by Nica, Speicher and Voiculescu. I had then the opportunity to meet there some of the most important mathematicians working in free probability, and to give a talk, thanks to which people in the field got to know about the subject of my research and my PhD thesis. After that I have received two offers for a post-doctoral position (from Texas A&M and from the University of Waterloo) and accepted the one from Waterloo (there I have started a long collaboration with Alexandru Nica, which resulted in several joint articles being published).

It was also in Banff that I first met Alice Guionnet from CNRS and ENS Lyon, and we ended up publishing two papers together until now - in Commun. Math. Phys. and Complex Analysis and Operator Theory - (we have another ongoing project). Also there I first met Benoit Collins from U. Ottawa, with whom I have published a paper (to appear in CJM), and James Mingo, from Queen's University, Kingston, with whom I have had many useful discussions in the years since. More recently, also in Banff, I started a collaboration with Dimitri Shlyakhtenko from UCLA.

I have had the privilege of two other participations at 6-day workshops in Banff. This led to several other very useful interactions with researchers from random matrix theory, free probability, von Neumann algebras, quantum computing and operator theory.

I think that the facilities of BIRS - excellent working rooms, ample space, enough peace and quiet for concentration, the convenient placing of the dining facilities - and the format of the workshop, with many talks, but also very much free time for private discussions among participants, are extremely useful for furthering research, and I am quite convinced that they were very good for my research activity since I was a student until now, when I became assistant professor.

It was always a pleasure and an honour to participate in BIRS' activities, and I wish BIRS good luck.

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Larry Smith, Professor Emeritus, Institute at Mathematisches Institut Universitaet Goettingen

I was privileged to participate at a conference at BIRS on fusion theory at which a number of finite group theorists, algebraic topologists, and a few invariant theorists were present. I think this was in 2005. I spoke with several people at this conference about some of the problems then of interest to me: in particular the search for a proper generalization of a result of Robert Steinberg on algebras of coinvariants of reflection groups from the complex case to the general case.

In conversations with Bill Dwyer and Clarence Wilkerson I explained the result of Steinberg and how my student T-C. Lin had succeeded in extending it to the case of finite fields whose characteristic did not divide the group order. Some months later Bill and Clarence posted a completely different elegant argument that extended the result to the general nonmodular case. Using techniques derived from the paper I was then able to find a first modular analog of Steinberg's result (this will appear soon in Forum Math).

I also discussed some results of Bob Stong and myself with Dave Benson and Peter Webb. From them I learned a great deal about the representations of $GL(n F_q)$ on the vector space $Mat_{n, n} (F_q) of n \times n$ matrices over the finite field $F_q$ that Bob and I had not known. This new information allowed us (Bob and I) to greatly simplify several arguments in our work on Poincaré duality algebras (to appear in Adv. in Math and the PAMS soon).

In short, the conference for me was a great success in that it helped me to improve and extend my research, as well as open my eyes to a new area of research, namely fusion theory from the topological viewpoint.

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Shigeo Koshitani, Professor, Department of Mathematics, Chiba University

I spent a week at BIRS from end of October to November 2003 attending the meeting``Current trends in representation theory of finite groups".

I gave a talk there, which was nice. However, what was much more wonderful was (and still is) that I could make several acquaintances, whose interests were close to mine. I could discuss our mathematics with those people there and then, and it still works quite well. My visit there then had been so useful important for my research. Especially because of what I announced there, I could write a joint paper with an American researcher in 2004. Actuallly, he was not there, but a person, who was in the auduience of my talk at the BIRS, informed my result to this American mathematician (Morton E. Harris), and then our collaborations started. The joint paper showed up in the Journal of Algebra (2006). That is, the collaborations really originated during the workshop in 2003. Therefore, I really appreciate it.

I might be able to visit the BIRS in 2011. I am looking forward to visiting the BIRS again so much.

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Christian Schmeiser, Professor, Faculty for Mathematics, Group Leader, Molecular and Systems Biology, University of Vienna.

Earlier this year I attended two BIRS workshops on very different subjects. The first meeting (on kinetic transport equations) had been attended by a very well selected group from an established international community. For me this meant both an efficient update on the most recent results and a possibility to further my international cooperations. In particular, one publication on hypocoercivity with Jean Dolbeault (Paris) was essentially finished in Banff. The second meeting (on Mathematical Biology) provided an excellent opportunity to meet new people in this strongly developing and very diverse field. A new cooperation has been started with Michael Ward (Vancouver) on the application of exponential asymptotics to a mathematical model for chemotaxis.

It goes almost without mentioning that the pleasant environment and perfect organisation (many thanks to Brenda Williams) greatly contributed to making my visits as successfull as they were.

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David McKinnon, Researcher, Department of Pure Mathematics University of Waterloo

I was an organiser for a workshop at BIRS in the late fall of 2008, and it was a wonderful experience. I'd been to BIRS before, as a participant, so I already knew that BIRS is a fantastic place to do mathematics. The area is breathtakingly beautiful, but most importantly, attending a BIRS workshop means spending five days in close proximity with other mathematicians in your area of expertise, with nothing better to do than invent new mathematics!

The workshop I helped organise was an excellent example of this. It was the first major international meeting devoted to the discussion of arithmetic properties of K3 surfaces, and it brought together mathematicians from disparate areas, both geographically and mathematically. My experiences at BIRS have been uniformly excellent, and I constantly exhort my colleagues to partipicate in and organise workshops at BIRS whenever they have the opportunity.

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Urban Larsson, Mathematical Sciences, Chalmers & University of Gothenburg

I participated in the Combinatorial Game Theory workshop 2008, January 20-25 (BIRS) has opened up a new territory of research for me. I am currently producing a paper, ``Wythoff Nim Extensions and Certain Beatty Sequences," that would not have come about had I not come to BIRS in 2008.

I am about to resubmit the paper that I was referring to (above). It has grown considerably since the BIRS-workshop in 2008, where it was presented for the first time. The workshop inspired me to develop this paper. Since then it has also been presented at CANT 2009 (CUNY) and Chalmers, Gothenburg, The Discrete Seminar (June 2009). But as I mentioned, BIRS was the major source of inspiration for this paper. This paper, that I hope will be included to the ``Games of no Chance 2008" publication, will most likely also be included in my ``LIC-Thesis" at Chalmers and Gothenburg University this autumn.

I already knew professor Aviezri Fraenkel, professor Richard Nowakowski and Neil Mackey however there are many new contacts that I would probably not have made otherwise such as Eric Duchene, Jorge Nuno Silva, Aaron Siegel, Richard Guy, Elwyn Berlekamp, Robert Hearn, Martin Demaine and many more.

I might just as well mention that my professional career as a mathematician had started for real roughly at the time of the BIRS workshop, so I cannot underestimate the importance it may have had. In my application for a PhD position at Chalmers one of the main merits that I mentioned was the workshop in Combinatorial Game Theory at BIRS. I was accepted just 5 months after the workshop, in may 2008. Thank you so much.

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Serge Tabachnikov, Professor, Department of Mathematics, Pennsylvania State University

Valentin Ovsienko and I spent a week at Banff in the late spring of 2008 doing Research in Teams project. The topic was the pentagram map, a projectively natural iteration on polygons introduced by R. Schwartz in 1992 and extensively studied by him (in 3 papers). Schwartz found experimentally that the dynamics of the map was quasi-periodic, a typical behavior for integrable systems, and he found a large number of integrals for the map. The missing part was an invariant symplectic structure, the search of which was our goal with Ovsienko.

In a week we managed to make a very important step: we found that the map, in the case of pentagons, had an invariant Poisson structure (rather than a symplectic one). Continuing this work, jointly with Schwartz, over the summer and fall of 2008, we found an invariant Poisson structure for all polygons which made it possible to explained the experimentally observed dynamics via Arnold-Liouville theorem. We wrote two papers, posted on the ArXiv; the shorter version appeared in Electron. Res. Announc. Math. Sci., 16 (2009), 1-8. During the past year, we gave several talks on the subject at various institutions including major international research centers (I. Newton Institute, Max-Planck-Institut, Oberwolfach). These talks were received enthusiastically.

We continue our study of the pentagram map focusing on its close, and somewhat mysterious, relations with discrete integrable systems and the theory of cluster algebras. Our participation in the Research in Teams program was the main factor in the breakthrough that we made in our research. In my opinion, the program is extremely valuable and should continue by all means!

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Javier Pena, Associate Professor, Operations Research, Carnegie Mellon University

The opportunity to participate in the workshop on positive polynomials at BIRS in fall 2006 was a major enhancement to my academic career. The exceptional facilities and work environment at BIRS provided a rare opportunity to meet and work with scientists in diverse areas of computational mathematics including real algebraic geometry, functional analysis, and optimization. Among many other benefits, a junior colleague of mine and I initiated the key ideas of what turned out to be an extremely fruitful research collaboration on financial applications of moment problems.

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Krzysztof Oleszkiewicz, Associate Professor, Institute of Mathematics, University of Warsaw

During last 4 years I participated in one workshop hosted by BIRS - ``Advances in Stochastic Inequalities and their Applications", June 7-12, 2009, organized by L. Devroye, G. Lugosi and D. M. Mason. Similar conferences were held in Atlanta, in 1997, and Barcelona, in 2002. Occasions to meet in one place and at one time so many specialists in this subject are recently quite rare - usually stochastic inequalities are treated as tools rather than an independent object of interest, which results in their being discussed separately, depending on their range of application rather than their specific nature. Therefore I appreciated the Banff workshop very much. I learned about some interesting new open problems and discussed old ones. I must admit that attending lectures remains the main source of my knowledge about progress in probability - published papers become longer and longer, and more technical, thus direct contact with authors helps a lot. What made this BIRS workshop different from most other activities I took part in, was its relatively relaxed schedule, leaving enough time for discussions, questions and rest, which made it much more reasonable and accessible than many densely packed programmes I attended. Last but not least, I must admit that beautiful mountain views, perfect organization and accommodation made my stay in Banff very nice.

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Henk Broer, Professor, Department of Mathematics and Computing Science, University of Groningen, Scientific Director, Institute of Mathematics and Computing Science

BIRS in my opinion is one of the finest facilities for scientific meetings that I know off. Here I am making a world-wide comparison. Apart from its practical things like accomodation, internet, etc., not to forget the magnificent natural environment, the opportunity to meet other scientists works out wonderfully well. I have attended a multidisciplinary workshop on life sciences and I still remember the contacts I had (being a mathematician) with outstanding biologists and medical scientists. One thing that was instructive to see is how mathematical modelling develops in different scientific communities and I was happy to be able to help a few colleagues out.

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Natasha Kirby, University of Western Ontario

In the spring of 2007 I attended a workshop entitled ``Mathematics and the Environment: Energy Risk, Environmental Uncertainty and Public Decision Making." The goal of this workshop was to address the world's environmental changes and concerns, and how mathematics can help model these changes as well as help make decisions about solving this global problem, even given the uncertainties involved.

As a first year PhD student it was wonderful to meet other graduate students as well as economists and mathematicians who were working on different aspects of this problem. The lectures were given by world leaders in their fields and the material covered was extremely relevant and also very interesting.

In addition, the atmosphere at the Banff International Research Station was perfect for learning and research. The accommodations were very comfortable and the scenery is of course breathtaking. This workshop increased my knowledge of the mathematics being used to address environmental issues and has certainly helped me in my current reseach, which involves financial modeling of alternative energy sources.

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Joseph A. Cima, Professor, Department of Mathematics, University of California at Chapel Hill

I visited the Banff research center for a week of collaborative research with professors I. Graham, S. Krantz and prof. Kim We spent one week working on a problem in invariant metrics on domains in $C^n$. This was a very positive week for all of us. We spent another three months finishing the project and it was published in the Nagoya Math.J. Vol.185(2007) (title ``The Caratheodory-Cartan-Kaup-Wu Theorem on an Infiinite Dimensional Hilbert Space").

Without this special week where we could sit together and discuss the approach and hammer out some of the more challenging details I think the project would have taken us more than 16 months to get the paper finished. It was a very great boon to our work on this problem.

I think the programs offered by the Banff research station are an excellent way of providing stimulus and help in promoting outstanding research in mathematics.

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Stefanie Petermichl, Assistant Professor, Department of Mathematics, University of Texas

I participated in a research group of four, Lacey, Pipher, Petermichl and Wick in March 2006. The resulting paper about higher order Riesz commutators appears in AJM this year. Our week's stay at Banff contributed considerably to our success, even though we worked on the text for over 18 months afterwards.

On a more amusing note:

I am also in the particular situation that I met my partner and father of my children during my stay at Banff. He was a participant of a large numerical analysis conference.

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Maarten van Emden, Adjunct Professor, Department of Computer Science, University of Victoria

I benefited from BIRS by my participation in the workshop on Constraint Programming, Belief Revision, and Combinatorial Optimization in May 2003. I almost didn't go because the combination of topics seemed, to say the least, puzzling. It turned out several other participants were in the same position. Right from the start it became clear that the workshop was made for people like us, that we had been restricting unnecessarily our field of view. I think only the format of the workshop and the environment provided by BIRS could have unleashed the synergies potential in bringing together these areas of research.

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Kurt Luoto,

I have had the pleasure of two visits to BIRS (so far).

The first was a two-week workshop for graduate students, in the summer of 2005 if I recall correctly, titled ``Computing the Continuous Discretely", which was run and taught by Matt Beck and Sinai Robins, authors of the subsequent book of the same title. In addition to learning some fascinating material regarding counting integer points in polytopes, I made many new acquaintances. I have kept in touch with several of the attendees since then, including Profs. Beck and Robins, who both have offered me advice as a graduate student. One of my acquaintances later became a collaborator on a pair of papers, though this collaboration did not arise directly from our experience at the workshop.

My second visit was in July of 2008. Jim Haglund, Steph van Willigenburg, Sarah Mason, and I made use of the BIRS facilities for a week with the hopes of proving some conjectures that we had regarding material we had been working on beforehand. The environment provided by BIRS was most conducive to progress. The week was extremely productive, and we proved everything that we had hoped for. We jointly have submitted two papers to journals based on the results from this week together.

In addition to providing an excellent environment for conducting research, it also happened that another much larger group was also using the BIRS facilities that week, namely a workshop for physicists and engineers working on the theory behind quantum computing. As it turns out, their work was not entirely unrelated to our field of research, the overlap being symmetric function theory. We attended a few of their talks and had some conversations with them over meals. Although neither of our respective groups made any direct contributions to the field of the other, and I am not aware of any continuing contacts between the groups, I think we each gained a little more perspective. I had the feeling that with just a little more understanding on my part, I could possibly contribute to one or two of the problems that we heard discussed in the talks. As far as I know, it was only by chance that our two groups happened to be at BIRS at the same time, but I like to think that the diversity of uses of the BIRS facilities makes these sorts of interactions between practitioners in different fields more likely than they would be otherwise.

I already know of yet another conference that I will be attending at BIRS in 2010 (regarding quasisymmetric functions). I very much look forward to it.

My sincerest thanks to you and the BIRS staff and all who make it possible and available to our community. Keep up the good work!

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H. Garth Dales, Professor, School of Mathematics, University of Leeds Anthony To-Ming Lau, Researcher, De[artment of Mathematical and Statistical Sciences University of Alberta Dona Strauss, Researcher, Department of Pure Mathematics, University of Leeds

It is with great pleasure that we strongly recommend with great enthusiasm that grants supporting the Banff International Research Station (BIRS) be renewed as requested.

BIRS, an innovative invention of Professor Nassif Ghoussoub, Director of BIRS, has had a very significant impact on mathematics worldwide through its various activities, such as 5-day and 2-day workshops as well as Research in Teams. Here is the list of some activities that we have been involved in personally during the last four years:

1. Two weeks of ``Research in Team” at BIRS in September 2006, and May, 2009. From works initiated in these workshops, we have successfully completed two memoirs authored by Dales, Lau and Strauss. One of them (201 pages) has already been accepted for publication as an American Mathematical Society Memoir, and the second was submitted a month ago.

2. A 5-day workshop organized by Eberhard Kaniuth (University of Paderborn, Germany), Anthony To-Ming Lau (University of Alberta) and Zhong-Jin Ruan (University of Illinois) on ``Operator spaces and harmonic analysis”, with participants from all over all the world. H. Garth Dales was there as an invited speaker.

3. Two 2-day workshops: ``Northwest Functional Analysis Symposium” mainly for graduate students, post-doctoral fellows, faculties and visitors in functional analysis at universities in Alberta, British Columbia, Saskatchewan and Washington. H. Garth Dales was an invited speaker in one of them.

The workshops at BIRS have always generated a lot of interactions among participants allowing them to make very significant progresses on their research.

We are very grateful for the opportunity that this has provided for us in our mathematical work : we have been stimulated and excited by what has happened during our visits to BIRS; the prospect of having an opportunity to visit BIRS has concentrated our minds on plans for research; the excellent conditions for research in Banff have meant that our visits there have always been very productive.

We believe that the opportunity to visit BIRS has solidified the existing strong links between the University of Leeds, UK, and colleagues in Canada. It is a particular benefit to Canadian mathematics (which sometimes struggles with the problems of geographic remoteness) that non-Canadians gain such a fine impression of Canadian mathematics from visits to Banff, and become even more enthusiastic about collaborations with Canadian mathematicians.

We should like to pay tribute to the courtesy that we have received from the administrative team at BIRS, and the quiet efficiency with which our visits have been organized.

We very strongly recommend that grants supporting the Banff International Research Station (BIRS) be renewed, as requested.

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Tobias Weth, Professor, Institute of Mathematics, Goethe-University Frankfurt

It is a pleasure for me to describe the impact of the two BIRS workshops I experienced in 2007 (on ``geometric inequalities" and ``elliptic and parabolic nonlinear PDE"). The period 2007-2008 marks a turning point in my career since I submitted my habilitation thesis, had numerous job interviews and received a call for a professor position in Frankfurt. During this time, it was extremely important for me to present my work in front of world leading experts. In both workshops I had the chance to give talks, and I received helpful and inspiring comments which stimulated a large part of my current research. There are many aspects and features which, from my experience, distinguish the BIRS workshops from other meetings. First, it is the actuality of the chosen topics which fits well with the impressive scientific quality of participants. This creates a special dynamic within the workshops where people communicate intensively and concentrate on big issues and on promising ideas. Moreover, it is the remoteness of the Banff Centre which is attractive to the mathematical community. Experiencing high scientific quality together with the pleasant atmosphere and the convenience of Banff Centre, I realized that this is a place where I can move forward and get inspirations for a broader study of my field. In particular, this feeling was present in the first workshop on geometric inequalities. Although geometric inequalities are not at the center of the research I had carried out before, I consider the underlying methods - in particular optimal mass transportation - to be highly effective also in the qualitative theory of nonlinear elliptic and parabolic equations. The workshop presented a unique chance for me to learn the new developments in the field and to exchange ideas from different methodological backgrounds. Without the workshop, I would still have no contact to people working on optimal mass transport. In sum, the workshops in Banff helped me a lot to enlarge my toolbox of mathematical methods, to put my own research into a larger perspective and to realize the potential and benefits of other approaches. I hope to be able to participate in many further BIRS workshops, because in my opinion BIRS is an ongoing story of success and mathematical progress.

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Thomas D. Pollard, Professor, Department of Molecular Cellular and Developmental Biology, Yale University

I participated in the 2005 Conference on Mathematical Biology of the Cell. As an experimentalist with lots of quantitative data, this conference was a splendid opportunity to meet a wide range of theorists whose work depends upon the type of data that we collect. I knew some of these mathematicians, but met some new friends as well. I not only learned many things from these mathematical colleagues but also established relationships that have continued to be useful as time passes. Conferences like this benefit both theorists and experimentalists. At least in my field, theorists have a huge challenge separating reliable from unreliable experimental data, so an opportunity to meet the people and discuss experiments is very beneficial. Knowing the personalities involved is valuable to both sides.

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Mary-Anne Spring Chief, Crowfoot School

I found BIRS informative and engaging. As a new teacher I found the math workshops especially helpful; learning how children percieve math as opposed to how we are are actually teaching them has helped me significantly in my grade 5 classroom. I have a degree in English, and if not for the workshop, I would not have come to enjoy teaching math as much as I do now. I especially enjoyed learning how native cultures used math and science daily and incorporated them into stories and legends. This knowledge or way of knowing helped them better understand and live off the land, to become organized and self-sufficient societies. If we can get back some of that, historical, natural, way of percieving the world scientifically, it would greatly benefit how our children learn in the schools.

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Neal Madras, Core Investigator, FRSC, Department of Mathematics and Statistics, York University

I have attended three five-day workshops at BIRS:

Statistical Mechanics of Polymer Models (2003) Critical Scaling for Polymers and Percolation (2005) Mathematical Immunology of Infectious Diseases (2009)

The 2003 and 2009 workshops were especially important for me:

The 2003 meeting exposed me to various researchers in the theory of knotting phenomena in polymers. Prior to the BIRS meeting, I had read some papers on this topic before, and I was not convinced that this area had much interest or scope. However, hearing the diverse talks on this subject in a short period improved my overall perspective, and made the area sound more intriguing. I have since worked on a few projects in this area, including one recently accepted paper, one recently submitted, and one in early stages. The BIRS meeting was definitely a factor in getting me more involved in this area.

The 2009 workshop is still very recent, but it has had an immediate (and probably long-lasting) impact on my research. I had been doing some work on immunology models as a consequence of my work on the MITACS epidemiology project, but at a fairly light level (jointly supervising a summer NSERC student with Jane Heffernan, and discussing a simple stochastic model with Beni Sahai). Jane and Beni co-organized the Banff workshop and invited me to attend, even though it was rather far from my main research activity. It was a highly enjoyable and stimulating workshop. It gave me excellent insight into the major modelling issues. I learned a lot: I had read about immunology before, but hearing all the Banff talks made the whole area make much more sense. My project with Beni, which had been pretty tentative before the workshop, took much better shape and expanded to merge with two other projects with two of Beni's other collaborators. I also had extended discussions with another researcher about the stochastic simulations she discussed; we spent some time rewriting her Matlab code for better efficiency, and we have since corresponded about her work. The BIRS workshop has motivated me to get much more serious about my work in immunological modelling, and to make it a more substantial part of my overall research program.

From a different perspective, as Chair of the Mathematical Competitions Committee of the Canadian Mathematical Society, it has been wonderful to have BIRS host the two-week Summer Training Seminar for Canada's International Mathematical Olympiad team. The teams and trainers and the CMS are grateful for BIRS' hospitality!

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Daniel Kral, Research Fellow, Institute for Theoretical Computer Science, Charles University, Czech Republic

BIRS Workshop 08w5079 Graph Minors

I took part in the workshop on graph minors organized by Banff International Research Station in September 2009. The workshop brought together world-leading experts in the area of graph theory and graph minors in particular and young scientists and student who just start their mathematical carrier. Talks at the workshop included survey talks of different areas related to graph minors as well as recent developments in the field. I have a feeling that I learnt a lot during the workshop and I have also learnt several new problems to consider in my research, in particular, during minipresentations at the beginning of the workshop; I like the idea that every participant says something related to his/her research at the beginning of the workshop in a 5-minute presentation a lot. This is a great way of introducing participants.

I spent most of my time in discussions with Zdenek Dvorak and Robin Thomas on our joint project related to a linear-time algorithm for coloring triangle-free graphs on surfaces. In particular, we finilized our SODA'09 paper on the subject during the workshop as well as we discussed possibilities of extending some of our results to classes of graphs with bounded expansion. All minor-closed classes of graphs have bounded expansion and this newly defined notion attracted a substantial amount of interest of researchers in graph theory (Zdenek Dvorak gave a short introductory talk to the area during the workshop).

As usual, the visit to BIRS was very pleasent and scientifically very enhancing. The station and the Banff center provide a perfect environment for meeting with a very intensive work on different mathematical subjects (combined with an opportunity of spending a week out of university campuses in the middle of wonderful Canadian nature, an opportunity so seldom for most of researchers). I am very much looking forward to visiting BIRS again as well as to new mathematical achievements that are awaiting at BIRS workshops.

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Mark Hoefer, Assistant Professor, Department of Mathematics, North Carolina State University

I had the pleasure of attending and presenting my research at a weekend workshop at the Banff International Research Station (BIRS) October 24 - 26, 2008. The meeting brought together senior researchers and junior investigators, such as myself, to discuss non-linear waves.

The meeting engendered a superb atmosphere for scientific discussions which helped to catalyze some research ideas of my own. These discussions led to a new collaboration with one of the other attendees and we have recently submitted a manuscript with future work ongoing. The formal and informal exposure to senior researchers in the field was invaluable for learning opportunities, scientific discussions, and career development. I hope to have more opportunities to visit such a worthwhile center of scientific inquiry and sharing.

BIRS is an ideal setting for scientific meetings which, even in just a weekend workshop, can facilitate new collaborations and spark interesting research ideas. I wholeheartedly support the mission of BIRS.

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Savdeep Sethi, Associate Professor, Department of Physics, University of Chicago

I am writing to express my support for the workshops held at the Banff International Station. I have attended several such workshops over the past few years and I have found them to be very productive. The atmosphere at the center permits a great deal of informal discussion which is excellent for fostering collaboration. In the most recent one I attended in February 2009 on ``Gauge Fields, Cosmology and Mathematical String Theory", I was able to develop a collaboration with Katrin Becker which resulted in a paper titled ``Torsional Heterotic Geometries". In addition, I had useful discussions with many participants like Chuck Doran who I do not meet regularly otherwise. I enjoyed the meeting a great deal and hope continued support for the program will be provided.

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Wolfgang Ebeling, Professor, Department of Mathematics, Leibniz Universität Hannover

I attended the BIRS-Workshop ``Spectral Methods in Representation Theory of Algebras and Applications to the Study of Rings of Singularities" (08w5060, September 7-12, 2008). The main aim was to bring together researchers from representation theory, Lie theory, and singularity theory to study links between these subjects. I am working in singularity theory and I'm not a specialist in representation theory. I was invited because it turned out that some of my results were related to representation theory of algebras. On this workshop I got to know many people whom I hadn't met before and discussions with them have been very useful for my research. The workshop has widened my knowledge considerably. As a direct upshot of the conference it was decided to pursue one of the links emerging during the conference at a mini-workshop at the University of Bielefeld in October/November 2008, where I was one of the lecturers. Another upshot was that I learned about a Priority Program of the German Research Foundation (DFG) on Representation Theory and I wrote a proposal immediately after the workshop. The experience I made during the workshop was very helpful in writing this proposal. The proposal was successful. Summarizing, the workshop was very valuable for me and had great impact on my further research.

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Murray R. Bremner, Professor, Department of Mathematics and Statistics, University of Saskatchewan

I am writing on behalf of my co-authors Irvin R. Hentzel (Iowa State University) and Luiz A. Peresi (University of Sao Paulo, Brazil). We spent two weeks at BIRS in May 2005 on a Research in Teams program entitled ``Speciality of Malcev Algebras". One paper resulting from the work we started at that time has recently appeared:

M. R. Bremner, I. R. Hentzel, L. A. Peresi and H. Usefi Universal enveloping algebras of the four-dimensional Malcev algebra Proceedings of the Conference on Algebras, Representations and Applications (Maresias, Sao Paulo, Brazil, August 2007) in Honor of Ivan Shestakov's 60th Birthday Pages 73-90, Volume 483, Contemporary Mathematics, American Mathematical Society Edited by V. Futorny, V. Kac, I. Kashuba and E. Zelmanov

Another paper on a closely related problem, that I wrote together with a former postdoctoral fellow, has recently been published online:

M. R. Bremner and H. Usefi Enveloping algebras of the nilpotent Malcev algebra of dimension five Algebras and Representation Theory (accepted 24 June 2008, published online 17 February 2009)

I am currently involved in further research in this area with Marina Tvalavadze, who has been awarded a PIMS postdoctoral fellowship for 2009-2010 to work with me at the University of Saskatchewan. We expect to publish at least two more papers on enveloping algebras of Malcev algebras.

All this work would most likely not have been possible without the very research intensive atmosphere during those original two weeks in Banff.

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Peter Benner, Professor, Department of Mathematics, Chemnitz University of Technology

I attended the BIRS Workshop on Model Reduction and Matrix Methods April 3-8, 2004, and will atthend the workshop ``Control and Optimization with Differential-Algebraic Constraints", Oct. 24-29, 2010.

The workshop in 2004 offered the possibility to meet several people working in the same area of methods, but in different application fields. Due to the latter, our usual conference schedules do not overlap. This lead to a variety of fruitful discussions, that initiated some collaborations (e.g., as an outcome I spend some part of my sabbatical in 2007 at MIT and the initiated collaboration is ongoing) and also dragged me to the application field of model reduction for circuit simulation and micro-/nanoelectronics, inspired by talks at the Banff workshop of people working in that field. The outcome had significant impact on my career as I successfully applied for two proposals in that area:

- EU project (Marie Curie Industry Host Fellowships) O-MOORE-NICE! (Operational MOdel Order REduction for Nanoscale IC Electronics) see http://www.tu-chemnitz.de/mathematik/industrie.technik/projekte/omoorenice/index.php?lang=de

and, more importantly:

- Research network within the BMBF (German Ministry of Education and Research) funded program ``Mathematics for Innovations in Industry and Services": SyreNe (System Reduction for Nanoscale IC Design), see www.syrene.org, which I coordinate.

Going this direction was certainly inspired by the BIRS workshop.

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Hans G. Feichtinger, Professor, Department of Mathematics, University of Vienna

So far I've joined two workshops at BIRS, both of which have been very informative, well organized and stimulating. It is the ideal environment for a research mathematician, and I am looking forward for the next event.

I also enjoyed two concerts of the ``musicians in residence" and since we are active in time-frequency analysis I am in fact looking into the possibility of applying together with Prof. Walker (USA) for a workshop in this direction.

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Peter Ashwin, Professor, School of Engineering, Computing and Mathematics, University of Exeter

I'm writing as one of the organizers of the workshop 08w5046 (Low Complexity Dynamics) that took place at BIRS in 2008. I can personally say I was very impressed with all aspects of the support for the workshop, from the pre-arrival information, support for inviting and logging details of participants, and the clarity as to what was and what was not included in the package.

The accommodation, both living and research/seminar rooms, were excellent and the setting and surroundings of the Banff Centre make it a very attractive place to invite speakers - we very easily obtained participation of a wide variety of top-quality international speakers that would have otherwise been a lot of work to bring together! In particular, the ``common room" focus encourages participants to interact productively and informally, and is a perfect complement to the formal lectures. Even though I was one of the organizers, I found it possible to fully engage in workshop and a number of my current research topics date from the workshop - this in itself is testimony to the excellent support I was given by the team at BIRS.

I believe BIRS is a top-quality international venue for mathematical research workshops and I hope that it continues to be so for the forseeable future!

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Arek Goetz, Professor, Department of Mathematics, San Francisco State University

Permit me to add an informal word to Professor Ashwin's comments.

After the Banff 08 May meeting that Peter Ashwin, Anthony Quas, and myself co organized, I informally spoke with at least five participants (three US based and two French based researchers). Each of them expressed an admiration for how the Center operated. We all noted that upon arrival, full attention can be devoted to scientific work, with no need for any administrative activity.

As one of the co-organizers, it was also a joy to note that requests for joining our conference came from a number of top researchers to a point where we could easily exceed the capacity of a workshop. The location and prestige of the Banff Center certainly played in important role in it.

Given another opportunity, I would gladly team up and co-organize another event in the near future.

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Neil McKay, PhD Candidate, Department of Mathematics, Dalhousie University

I have participated in workshops at BIRS on two occasions. First, I was a student at a 5-day workshop run as a `winter school' and second, as a regular attendee at a 5-day workshop that was closer to conference than the previous one. As a grad student, first as a master's student and then (and now) as a PhD student, I really value the contacts and avenues of collaboration I've gained. I communicate regularly with people in many different places that I first got to know through BIRS. At both workshops, I also met, had dinner and conversed with very big names in the field (the field of each respective workshop).

The setting and facilities provided at BIRS encourage and enhance collaboration far more than a standard conference. I find the time I've spent at BIRS so enjoyable and productive I'm looking forward to the next time I might get to attend, should the opportunity arise.

Keep up the good work.

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Nitu Kitchloo, Associate Professor, Department of Mathematics, University of California, San Diego

I want to express my most enthusiastic appreciation for the Banff Research Station. I have been to it multiple times and found the period to be very productive. In addition, I found that the staff make the environment very relaxed and research conducive. BIRS is certainly a place that I would rank among the best research enviornments in the world. Thank you for your leadership in keeping it active.

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Yael Karshon, Professor, Department of Mathematics, University of Toronto

I participated in two BIRS conferences, one as organizer and one as participant and speaker. Both experiences were great.

An MSc student from Calgary attended one of these conferences, found it inspiring, and came to do his PhD in Toronto with me.

As organizer, I was not the ``main" organizer - the initiative came from another organizer, from the U.S. but I was so inspired by the place that on my way back I started making notes for another conference that I might want to organize in BIRS in the future. (This hasn't happened yet because I've been busy but I'm certainly keeping this in mind.)

And I can add the usual stuff. I learned new math and had good discussions; between and after talks I made progress with ongoing projects with collaborators who were at the same conference.

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Roger Fenn, Professor, Department of Mathematics, University of Sussex

I have attended a conference [at BIRS] and I have been impressed by its professionalism and the ease with which the surroundings are conducive to my scholarship and research. I hope that the centre can continue this progress and support more meetings in my field of low dimensional topology.

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Ivan Penkov, Professor, Department of Mathematics, Jacobs University Bremen

I have been in Banff twice in the last decade and both visits have been very fruitful for my research. Recent joint work of mine with I. Dimitrov and E. Dan-Cohen originated during our last visit as a ``research pair". This last visit was very stimulating. Thank you!

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Christopher Hacon, Professor, Department of Mathematics, College of Science, University of Utah

I have participated in 1 conference at NIRS. It was very interesting and nicely run. During this conference I started a collaboration with V. Alexeev which ultimately ended in the following publication:

MR2289869 (2008f:14028) Alexeev, Valery; Hacon, Christopher; Kawamata, Yujiro Termination of (many) 4-dimensional log flips. Invent. Math. 168 (2007), no. 2, 433-448

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Kaori Tanaka, Assistant, Department of Physics and Engineering Physics, College of arts And Science, University of Saskatchewan

I participated in the University of Alberta Theoretical Physics Institute Symposium in 2003, and gave a talk. It was a very interesting experience, meeting with people and listening to talks from a variety of different disciplines of theoretical physics. I met several people there, some of whom I now plan to collaborate with.

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Antoine Mandel, Researcher, Postdam Institute for Climate Impact Research

I attended the summer school on Mathematics and the environment a couple of years ago while I was a PhD student. The interdisciplinary exchanges we had then where instrumental for me in the writing of my PhD and I developed contacts which proved very useful during my post.doc.

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Louis Lemieux, Professor, Institute of Neurology, Department of Clinical and Experimental Epilepsy, University College London

This was my first BIRS event and I think it's a fantastic setting for scientific workshops.

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Jeremy Louis Marzuola, Department of Mathematics, Hausdorff, Center for Mathematics, University of Bonn

Probably the most important collaboration that came out of my time in Banff is that with Andrew Hassell, which resulted in the publication:

Eigenfunction Concentration for Polygonal Billiards Andrew Hassell; Luc Hillairet; Jeremy Marzuola Communications in Partial Differential Equations, 1532-4133, Volume 34, Issue 5, 2009, Pages 475 – 485.

I hope to see Banff programs thriving for a very long time to come.

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Michael C. Frank, Researcher, Massachusetts Institute of Technology

I just returned from a meeting at BIRS on Probabilistic Models of Cognitive Development. The meeting was a great success. The many interesting talks gave me a broad view of developments in this field, the shared meals allowed me many opportunities to interact with senior colleagues and discuss ideas from the presentations, and the beautiful setting encouraged evening hikes for extended interaction. Over the course of a week-long meeting I was able to cement a collaboration with one senior colleague, who I had not been able to correspond with effectively over email, and meet with several other collaborators as well. I really appreciated the opportunity to participate in the meeting and have raved about BIRS to my colleagues back at home.

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Yihong Du, Professor, School of Science and Technology, Mathematics Section, University of New England

It is my pleasure to testify that the Banff workshop I attended in Oct. 2007 was very valuable for my research. I was able to exchange information about research progress with many other participants at the workshop in an environment which stimulates new ideas. In particular, I was able to discuss with Prof. H. Matano (Univ. of Tokyo) about further research on our joint work, which led to a positive answer to a question posed by Prof. H. Brezis.

I very much hope that BIRS can continue to hold such workshops in the future.

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Stephen Mitchell, Professor, Undergraduate Program Director, Department of Mathematics, University of Washington

The conference/workshop on Schubert varieties at BIRS in March 2007 was one of the best conferences I have ever attended. As a topologist I am trying to forge some new links between topology and the many fields involved in the theory of Schubert varieties--combinatorics, algebraic geometry, Lie theory--and in this regard the conference was a spectacular success. The talk I gave on joint work with Sara Billey (a combinatorialist) was well received and led to many productive conversations that have inspired me ever since. I had the opportunity to meet with leaders in the field, for instance Frank Sottile and Alan Knutson, as well as many more junior researchers, particularly Megumi Harada, Julianna Tymoczko, Linda Chen, Tara Holm and Rebecca Goldin. The fact that these last five and Billey are women is especially noteworthy. It is unusual (in my experience) and encouraging to find so many talented women mathematicians in one place, and I think that BIRS as well as the organizers deserve credit for making this happen.

With the exception of Billey (a University of Washington colleague with whom I have two joint papers), no joint work has come out of this, but useful conversations have continued. In particular, Harada and Tymoczko have visited Seattle, I've visited Chen in Philadelphia, and we've invited Holm and Goldin to visit Seattle (although it hasn't worked out yet). Goldin is a co-organizer of a workshop on equivariant cohomology at AIM next March, to which I have also been invited. I doubt that any of this would have happened without the Banff conference.

The beautiful setting and excellent facilities certainly contribute to the success of BIRS. Even more important, however, is the fact that the participants live on-site, all gather at meals, and all have a common meeting place in the evening. This is in contrast to MSRI, for example, and greatly enhances the social interaction that is such a big part of mathematical research.

I very much look forward to visiting BIRS again.

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Brian Marcus, Professor, Department of Mathematics, University of British Columbia

I was co-organizer of a BIRS workshop in 2007. The facilties, staff and atmosphere were all excellent. The workshop led to several new results (some obtained on site during and between open problem sessions). These results, as well as others, will be contained in papers to appear in a workshop proceedings volume, edited by the workshop organizers, which will be published by Cambridge University Press in 2010.

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Oksana Yermolayeva, Center of Mathematical Research, University of Montreal

I am postdoctoral fellow, working presently in Europe. I have participated in the 5-day conference titled ``Quadrature Domains and Laplacian Growth in Modern Physics", (07w5008), from July 15 to July 20, 2007.

Inspite of the many other international conferences I have attended, this one was by the present time, the unique event, which scientific organization overcame any hope.

All specialists where from diverse disciplines: from potential theory, geometric function theory, special functions over complex domain, probability, operator theory, stochastic processes, random matrices and modern field theories.

All talks beared interdisciplinary and at the same time, adjacent subjects, that enriched the global understanding of the subject of the conference at whole.

I consider these five days in Bannf to have been a very important event that widened my scientific horizons and motivated new interests in the theory of Schwarz function and Stochastic Loewner evolution. New results on Stochastic Laplacian growth were produced in 2008. In that same year, I received financiation for the research project in Europe on the same subject.

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Patricia Blanchette, Associate Professor, Department of Philosophy, University of Notre Dame

I am writing to express my thanks to BIRS for hosting a very good and important workshop in which I was fortunate to participate.

In February of 2006, I participated in the workshop entitled ``Mathematical Methods in Philosophy," held at BIRS and coordinated by Aldo Antonelli, Alasdair Urquhart, and Richard Zach. The workshop was unusual in bringing together philosophers and mathematicians from quite different fields of expertise, but all of whom approach a core of philosophical questions via the techniques of modern mathematics and mathematical logic. For myself, I learned a good deal about recent developments in the use of mathematical methods in formal theories of truth. Also, and most importantly for my current area of research, I had the unusual opportunity to speak informally with such mathematicians as Yannis Moschovakis on the kinds of philosophical topics which motivate much of their research, but which don't generally find their way into print. Moschovakis' work on synonymy and its role in formal systems is especially relevant to my current work (recently culminating in a book manuscript now under review) on the work of Gottlob Frege on logic and conceptual analysis.

The conference was, in short, an unusual opportunity to learn about a good deal of recent work in a cross-section of fields very important to my own research interests and rarely brought together in a single venue. The workshop was also very pleasant and well-run. I hope to have the opportunity to come to BIRS again

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Izuru Mori, Associate Professor, Department of Mathematics, Shizuoka University

I visited BIRS to attend the workshop ``Interactions Between Noncommutative Algebra and Algebraic Geometry’’ from October 26 to October 31, 2008. Leading experts on this subject gathered together to this workshop from all over the world to study and to discuss topics related to the subject. BIRS is located in the very beautiful natural geography of the Canadian Rockies. However, what I appreciate most is its excellent environment that facilitates focus on research. We were able to do research for 5 days, 24 hours a day, without any interruption. There is no need to commute between the workshop site and hotels or to go out to look for restaurants to eat. We were able to listen to many interesting talks on new results in the workshop. In addition, discussions with collaborators after talks were very stimulating. In fact, a new idea I was inspired with in this workshop turned out to produce a new paper, which was submitted a half year after the workshop. For me, this workshop was one of the most fruitful opportunities to promote my research. I certainly want to visit BIRS again if there is another chance!!

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Fabio Ancona, Professor, Department of Pure and Applied Mathematics, University of Padova

I took part in the 2006 workshop in ``Hyperbolic Systems of Conservation Laws and Related Problem", organized by Gui-Qiang Chen, Walter Craig Constantine Dafermos and Konstantina Trivisa. It was the first time I visited Banff research center and it was quite a fruitful and enjoyable experience. The facilities are quite appropriate for hosting an event of this type which forsees both the presentation of new results and the possibility of free discussions about new problems and possible future collaborations among the participants. Indeed, it was for me a great opportunity in particular to communicate my undergoing research line concerning control problems for hyperbolic equations and to start discussing with some of the participants the possibility of analyzing new problems within this perspective and to initiate some collaborations in this direction. I really hope and strongly encourage the continuation and further improvement of the research activities at Banff which, surely, are providing an excellent and precious service to the whole scientific community.

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Charles E. McCulloch, Professor and Head, Division of Biostatistics, Department of Epidemiology and Biostatistics, University of California, San Francisco

I have just completed a 5 day workshop at BIRS: Emerging issues in longitudinal data analysis.

What a wonderful facility and staff!

Ours was a 5 day workshop with about 50 participants. I so much prefer the format that BIRS allows over the overly hectic, overly broad typical professional meetings. Invariably at such meetings I feel rushed to go from one session to the next, listening to speakers hurriedly trying to convey their ideas in 12 minutes, usually running over their allotted time with no chance for interaction or substantive questions.

BIRS was the opposite: a chance to truly interact and share ideas. I got to meet and exchange ideas with experts in my own area, with whom I had only had brief interactions in the past.

Thanks for the opportunity to have participated.

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Peter Lancaster, Professor Emeritus, Faculty Professor, Department of Math and Statistics, University of Calgary.

I write in support of the programmes conducted by the Banff International Research Station. I have participated in a few BIRS workshops and helped in the organization of two. I have also participated in similar activities elsewhere in Canada and internationally. The facilities offered at BIRS are world-class, and I believe that BIRS makes efficient use of them with its format of workshops (5-day and 2-day), focussed research groups, and so on.

I am also favourably impressed by the breadth of subject matter (in the math sciences) appearing in the BIRS programmes. The location in Banff is, of course, a great drawing-card which helps to ensure the participation of world leaders in the math sciences. The environment and programme-planning also foster easy communication between all participants.

I see BIRS as an important example of support in Western Canada for basic and applied science.

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Robert Moody, University of Alberta

It amazing how quickly the time has seemed to pass since we obtained our first funding from ASRA, NSERC, and the NSF for creating and operating BIRS. I was privileged to be involved with the creation of BIRS, the choosing its programming for the years of 2003 - 2005, and the day-to-day operations of BIRS during its first year of operation.

No doubt the greatest pleasure from all of this was to see the actual BIRS events running. Each week a new group of participants would arrive and in each case its participants immediately fell in love with the facility and its wonderful amenities. In each case we were in for a week of research-intensive mathematics attended by some of the finest minds on the planet. I cannot think of an event in which the participants were disappointed by what they achieved, and there were several events in which they were absolutely ecstatic about it. BIRS encourages events that bring new people and new disciplines together, and in some cases the mix was just outstandingly successful.

One of the particularly attractive features of the way BIRS is arranged is that event organizers need only worry about the scientific side of things. All the petty details of invitations, room and board, etc. are handled by the staff at PIMS and BIRS. Likewise for participants - all they need to do is get themselves to Banff. The rest is looked after. No wonder that there has been such a high demand for workshop slots (consistently over 2:1 ratio of applications to slots available, and for 2006, 2.5 : 1).

Another reason that BIRS has been so successful is the quality of the local staff - really outstanding. Andrea is a wonderfully genial and efficient host, and Brent has produced a local computer system that is a source of constant praise from our visitors. I recall that in the early days, when everything was not yet quite perfected, one particularly well-known organizer said to me just as he was arriving that he had a few things to discuss with me about the way things were done. At the end of the conference I finally caught up with him and asked him what tell me what was on his mind. He said, ``Robert, I have only one thing to say about this place -- it's fantastic!"

One of the things that I am particularly proud of is the way in which BIRS serves four different communities in such a nice way. First and foremost, it is an INTERNATIONAL research station. Every workshop attests to this fact. But we know that it is the North American community that accounts for the majority of the users, and this is as it should be: BIRS was to some extent a response to the famous MFO in Oberwolfach (Germany) and CIRM at Luminy (France), which had done so much for European mathematics.

The insistence that all BIRS events have a Canadian amongst the organizers has led to a significant presence of Canadians at every meeting. The local PIMS community has benefited too. Of course PIMS has a direct say in some 12 weeks of the yearly programming, but a quick look at the record will show that PIMS researchers are organizers involved in far more events than that. This is not due to favouritism on the part of the BIRS Scientific Review Panel. The BIRS panel pays no attention to anything except scientific quality and scientific balance across the mathematical sciences. But of course our local community has many strengths and consistently comes forth with many good proposals each year.

Beyond this there are the two day events, squeezed between the regular five-day workshops, which have provided a cost-effective way of supporting the local PIMS and Alberta communities, as well as providing a facility for events of particular timeliness. I think here, for example, of several workshops for teachers in Alberta and British Columbia, and the mini-conference on SARS, which led subsequently to a full-fledged workshop at BIRS.

Beyond these events, BIRS hosts a program of research-in-teams. This allows small groups (2 to 8 people) time to escape from the usual stresses of their university or research institutions to work on difficult problems in a sustained way or to finish large projects, like books, which just need uninterrupted time. I have always been a big supporter of research-in-teams, since I have had been on a similar program at Oberwolfach several times. Each time was just fantastic - we got so much done, maybe three times as much as we could have done if we had met in our own institutes. I know from talking to those doing the same thing at BIRS that this type of program is deeply appreciated by those who used it.

Thus I think that in all respects BIRS has been what we all had hoped it would be - in fact even more. For its modest cost (in terms of what science costs in general) BIRS is terrific value for the money. It already has an international reputation, even to the extent that the MFO, the CIRM, and BIRS are now spoken of in equal terms. With its glorious location and the surrounding culture of the Banff Centre, it is unique.

I worked with the BIRS project for three years, including being on-site most of the time during its first full year of operation. I left the project, once that I felt that my job was done. Still, whenever I sit in the dining room of the Banff Centre, gazing at the Rocky Mountains in the background, I think back to the creation of BIRS and I can only feel that it was a miracle. It is a wonderful treasure for North America, Canada, and the PIMS community. Long may the miracle continue!

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Tucker Carrington, University of Montreal

I attended a workshop at BIRS about one year ago. Participating in the workshop gave me the chance to meet other scientists working in similar fields. The workshop was run extremely well. I strongly support the renewal of BIRS.

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Raphael Bousso, Assistant Professor, Department of Physics, University of California

I attended the BIRS workshop on string theory and cosmology in June. It was an extremely valuable experience. Workshops of this format are in my view by far the most useful way of organizing a meeting: put a few dozen people in an isolated environment and watch the sparks fly. Certainly a few flew my way; indeed, the workshop influenced the focus of my research, moving it from more formal considerations back to fundamental questions of cosmology. Two papers which I am now finalizing and which I expect will appear in the next few weeks are the direct result of this process.

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Karl Petersen, Department of Mathematics, University of North Carolina

I very much enjoyed the week I spent at BIRS in July 2003 as a participant in the workshop on Joint Dynamics. The setup and hospitality are just wonderful, allowing for formal sessions as well as informal interactions, especially in the breakfast/lounge area and the conference rooms. The computers and connections in the individual rooms are extremely useful. As a result of that stimulating environment, I thought about the joint action of the shift and odometer on the space of infinite two-sided sequences of 0's and 1's. I will be speaking about the first results at the School on Information and Randomness in Santiago, Chile, in December 2004 (this month). I am conducting further research on how things would change if the odometer were to be replaced by the Pascal adic. One or more publications will result from this work. I very much look forward to my next visit to BIRS. I wish I could get there this summer for the Bridges workshop, but I am likely to be in Europe at that time.

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Bruce Reed, Canada Research Chair in Graph Theory, McGill University

I would like to express how important I think BIRS is to the Canadian mathematical community. The events organized there play a seminal role in fostering contacts and germinating new research directions. By taking the organizational and financial burdens off the shoulder of the researchers, BIRS makes these events much more likely to happen. Having the centre at a world renowned beauty spot helps to ensure the participation of top mathematicians who must turn down many invitations every year. I think it is imperative that this programme be continued and extended as much as possible.

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Bruce Shepherd, Bell Labs

I participated in the previous year, and I believe I gave my feedback at that time. However, let me just summarise and say how fruitful (and enjoyable) the workshop I attended was. I wish you the best of luck on the renewal.

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Robert E. Kass, Department of Statistics, Professor, Department of Statistics, Carnegie Mellon University

BIRS was a great opportunity for me to discuss research with some people doing related work, people I had not previously been able to meet. It has led to an extended visit for me in the department of one of the principals, which I am looking forward to and which I presume will be productive.

Good luck with the proposal.

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Ryan Haskett, Duke University

Banff was simply the nicest (and most beautiful) conference area I've been to. The facilities and service was very good. The computers in the room were a nice touch as well so I could keep my numerical computations going during the conference.

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Robert J. Elliott, RBC Financial Group Professor of Finance, University of Calgary

I am very pleased to write in support of the Banff International Research Station. Situated in a picturesque location as part of the Banff Centre, the Research Station provides hospitality and lecture rooms for high level research conferences in mathematics. The atmosphere is particularly conducive to fruitful discussions and interaction. Having taken part in such meetings I can say they are very valuable. One of the most useful aspects of a recent meeting on Financial Risk was the participation of people from the energy companies in downtown Calgary. Their presence helped clarify and define problems of interest.

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John R. Klein, Wayne State University

I have thus far participated in 2 BIRS workshops, and I am delighted with the way the institute is set up. The staff is very congenial, and Banff is an fun place to do mathematical research. The one thing which needs to be developed, I think, is a mathematics research library.

Until BIRS, there was no place in North America which could compete with Oberwolfach mathematical conference and workshop facilities. I believe that BIRS is destined to fulfil the role that Oberwolfach plays in Europe.

Long Live BIRS!

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Savdeep Sethi, Assistant Professor of Physics, Enrico Fermi Institute, University of Chicago

I attended a BIRS workshop on string theory and mathematics in the last year. It was a pleasurable and stimulating experience; particularly, because of the interdisciplinary nature of the program. I would strongly support future BIRS workshops of this kind.

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Antonio Sa Barreto, Professor, Department of Mathematics, Purdue University

The meeting I attended at BIRS was very helpful to my research. I gave a talk on the subject I was working on and had a chance to talk to several people there, including Rafe Mazzeo and Robin Graham, about what I wanted to prove. Sometime later, and partly because of those conversations, I was able to prove the result I wanted. The paper entitled ``Radiation Fields, Scattering and Inverse Scattering" (http://xxx.lanl.gov/math.AP/0312108) is to appear in the Duke Math Journal.

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Victor Ivrii, Professor of Department of Mathematics, University of Toronto

Honestly I was rather reserved about BIRS when the idea came first. Then at the beginning of 2003 I participated in the workshop and was converted. In accordance to the request of Robert who was then the Director of BIRS station I sent the message that very important progress in my work

Sharp Spectral Asymptotics for Operators with Irregular Coefficients. IV. Multidimensional Schrödinger operator with a strong magnetic field. Full-rank case ($>$ 80 pp) was done during BIRS workshop.

Nothing much to add to this except: in the Summer 2003 my son Oleg was in BIRS (IMO training camps) and he and those his teammates I know were absolutely excited by their stay. Would be it helpful if he wrote something too?

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Andrew Park, PDF Epidemiology, Dept. Biology, Queen's University, Dept. Math and Stats, York University

I attended a special program in infectious diseases in the summer of 2004. this was a unique opportunity to bring together scientists and mathematicians with a wide variety of experiences. The venue was excellent both in its strategic, beautiful location and in its modern, community-style structure.

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Chi-Kwong Li, Professor, Department of Mathematics, The College of William & Mary

I have attended two BIRS workshops in 2003-04, and I had wonderful experience.

In Nov. 2003, I attended the workshop on eigenvalues and singular values. It gave me a chance to describe the most current theoretical results in the study of eigenvalue and singular value inequalities to the numerical linear algebra colleagues. In return, I learned more about problems and concerns in numerical linear algebra. These broaden my outlook of research on the topic. As a result, I have collaborated with more colleagues on numerical linear algebra leading to the following papers:

1. C.K. Li and R.C. Li, A Note on Eigenvalues of Perturbed Hermitian Matrices Linear Algebra Appl., to appear.

2. Z.Z. Bai, G. Golub, and C.K. Li, Optimal Parameters in Hermitian and Skew-Hermitian Splitting Method for Certain Two-by-Two Block Matrices, submitted. 3. Z.Z. Bai, G. Golub, and C.K. Li, Convergence Properties of Preconditioned Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Semidefinite Matrices, submitted.

In May, I attended the Combinatorial Matrix Theory workshop. Again, it was helpful for me to exchange my experience and results with other colleagues. In particular, my recent solution on the open problem about 5x5 full ray nonsingular matrices was made better known. (Reference: C.K. Li, T. Milligan, and B. Shader, Non-existence of 5X5 full ray nonsingular matrices, Electronic Linear Algebra 11 (2004), 212-240.)

Also, I learned new problems and ideas from colleagues, and I am still currently working on some open problems presented in the meeting.

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Petra Klepac, PhD Candidate, MIT/WHOI Joint Program in Oceanography, Biology Department, Woods Hole Oceanographic Institution

BIRS made irreplaceable contribution to my studies and my PhD research. In summer 2004 I participated in PIMS-MITACS-MSRI Special Program on Infectious Diseases Summer School. The faculty at the summer school were the leaders in theoretical epidemiology from all of North America. I have not only learned about the ``hot topics" in the field, but I also had an opportunity to discuss the specifics of my dissertation research with these experts.

This experience was crucial for my PhD progress and I hope BIRS will continue organizing such successful mathematically oriented workshops in the future.

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Jinqiao Duan, Professor, Department of Applied Mathematics, Illinois Institute of Technology

I enjoyed my BIRS visit very much:

1. The research-in-team activity that I participated helped to push forward the very new area of invariant manifolds for stochastic partial differential equations We have two papers in press (resulting from this activity):

J. Duan, K. Lu and B. Schmalfuss, Invariant manifolds for stochastic partial differential equations (PDF). Annals of Probability 31(2003), 2109-2135.

J. Duan, K. Lu and B. Schmalfuss, Stable and unstable manifolds for stochastic partial differential equations (PDF). J. Dynamics and Diff. Eqns 2004, Vol. 16, No. 2, in press.

2. The activity also helped me to design a new course in stochastic partial differential equations:

http://www.iit.edu/ duan/courses/545text

Jinqiao Duan, Professor Department of Applied Mathematics Illinois Institute of Technology

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Michael Singer, North Carolina State University

I attended a Banff Workshop in Model Theory in the Winter/Spring of 2004. This is not my main field of research but I have needed, more and more, results and techniques from this area for my own research program. Attending this workshop allowed me to have face-to-face interaction with the experts who were able to direct my attention to the appropriate concepts and references (and clarify my misconceptions). My present work would not have come to fruition without this experience.

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Francois Labourié, Membre de l'Institut Universitaire de France, President du Departement de Mathematiques de l'Universite Paris XI

I participated to the conference ``New Techniques in Lorentz Manifold" in BIRS. I found that the working conditions were excellent. On a material level first (lodging,computer access, help from the staff), but more importantly on a scientific level. The BIRS center is a remarkable place for discussions both formal (conferences) and informal, mainly thanks to the fact the lodging is integrated in the conference center. It is definitely comparable on that grounds to CIRM in France and MFO in Oberwolfach (and certainly superior to other conference centers I have visited ...).

I came back from that conference with new ideas that I hope I will make fructify in the near future. I strongly support BIRS renewal.

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Pramathanath Sastry, Associate Professor (CLTA), University of Toronto

I participated in a BIRS RIT program in August 2003. The official number was 03rit005 and the title was ``Variance of quasi-coherent torsion Cousin complexes". The other members of the team were Professors Joseph Lipman and Suresh Nayak.

Our time at BIRS was *extremely* critical to our research. We had a broad outline of what we wished to do, but we knew it would take more than 100 pages of manuscript, and this needed close cooperation and ``face time". In the end the manuscript we produced (three papers to appear in AMS's contemporary mathematics) is 276 pages (more than double the estimate we had). We would certainly not have been able to nail the issues, work through the details, and come up with new ideas (which extended the scope of the original plan) if it hadn't been for our time at BIRS. The natural beauty, and the efficient organisation were just what we needed.

I have already (unsolicited) sent a testimonial to Professor Ghoussoub. The manuscript that I am talking about can be downloaded from www.math.purdue.edu/ lipman/CONM.pdf if it helps with any upcoming review.

Please once again accept my heartfelt thanks for giving us the opportunity to finish this work. I very much doubt if we could have done it without the help of BIRS.

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Richard Kenyon, Department of Mathematics, University of British Columbia

my week at Banff in June, 2003 was an excellent research opportunity for me, and I had a very fruitful collaboration with researchers there. In particular with Boris Solomyak and Lorenzo Sadun we have a joint paper based on work we started while there: ``Topological mixing for substitutions on two letters", submitted to ETDS. Moreover it gave me an opportunity to present my recent work on statistical mechanics to a community of dynamicists who would not ordinarily have known about this work, since the two fields, although close to one another, usually have distinct conferences and workshops.

I am co-author of a proposal for a BIRS research conference, and I find this venue is really the best way of getting colleagues from around Canada and the US together. It makes the job of organizing a conference significantly easier.

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Matthew Hedden, Department of Mathematics, Columbia University

In the Fall of 2003, I attended an MSRI hot topics workshop at BIRS on Heegaard Floer Homology and Gauge Theory. At the time I was a third year graduate student. This conference and the experience with BIRS had a profound impact on my mathematical development. The accommodations and organization of the conference served as the perfect environment for an intense and stimulating mathematical experience. At this workshop I proved my first theorem, due in large part to the excitement and intensity of the conference. I view the conference as a turning point, or more accurately as the starting point, for my mathematical career. I would love to come back to BIRS for similar experiences in the future and hope that it will exist for others, as well.

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Anne-Gaelle Rolland-Lagan, Department of Computer Science, University of Calgary

I attended a PIMS meeting for postdoctoral fellows at The Banff International Research Station (BIRS) in April 2004. This was a particularly enjoyable place for the meeting to be held, with great computing facilities, and great working and recreational areas designed to favor the exchange of ideas between participants. The meeting I attended at BIRS was particularly useful, as it allowed me to exchange with other postdoctoral fellows in a great atmosphere, and I did take home valuable advice, in particular on how to make a successful transition from a postdoctoral fellowship to an assistant professorship.

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Zhongshan Li, Associate Professor of Mathematics, Georgia State University

I found the Workshop on Combinatorial Matrix Theory sponsored by BIRS most stimulating and pleasant. I talked with many other participants there; such exchange of ideas was very beneficial to my research projects.

The mathematics community is indebted to BIRS for offering many exciting and stimulating workshops.

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Adrian Butscher, Department of Mathematics, University of Toronto at Scarborough

I participated in the BIRS workshop on Geometric Evolution Equations (GEE) in July of 2004 that was organized by Klaus Ecker and Ben Chow. At present, GEE is a dynamic and very relevant area in Riemannian geometry and geometric analysis because of recent advances in the field stimulated by Perelman's discoveries. I am not an active researcher in GEE, although it is a great interest of mine. I thus benefited enormously from interacting with the leading researchers in GEE who were assembled in Banff for the workshop. Furthermore, I identified an area in which GEE overlaps with my own research, and an idea for a future research paper was born. I have since been invited to another GEE workshop by the researcher with whom I discussed this idea at Banff, and we will investigate the idea further.

Please consider me a strong supporter of BIRS and the role it plays in uniting mathematicians both internationally and within Canada.

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Hamid Bolouri, Professor of Computational Biology, Institute for Systems Biology

I am writing to express my enthusiastic support for further funding of the The Banff International Research Station. As a former participant, I applaud the efficiency of the organization at BIRS and the wonderful environment it provides for true scientific interaction. The workshops at BIRS present a unique opportunity for leading researchers to discuss well-focused topics, spend extended periods together, and go well beyond the superficial exchanges that dominate most other meetings. BIRS also enriches Canadian research and academia by bringing international researchers to its meetings. I cannot think of a better way to encourage good research in Canada!

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Steve Harris, Saint Louis University

I participated in the BIRS workshop in New Directions in Lorentzian Manifolds. I found the conference materially helpful to me in my discussions with one of the Workshop leaders, Virginie Charette: Together we were able to determine that in my examination of group actions on Euclidean space, I had exhausted all the possibilities that fit my needs, so that I know that I must look to group actions on other spaces in order to get new examples for my boundary methods. (This was the answer to one of the open problems that I posed at our workshops problem session.)

I also initiated contact with Charles France, who posed a question to me that I was able to give a partial answer to while at the workshop. This may become the kernel for future work.

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Paul Monsky, Brandeis University

The workshop I participated in this September was very useful to me. I met with Hara for the first time, and it turned out that the theory of p-fractals developed by Teixeira and me was just what he needed to prove the rationality of a certain invariant he had been studying. (We will have a joint paper on this.) I also met one of my co-authors, Moira McDermott, for the first time, and renewed old friendships with Buchweitz,Miller, Watanabe and others. Quite apart from this, the calmness and beauty of the area does one good.

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Michael Overton, Professor of Computer Science and Mathematics, Courant Institute of Mathematical Sciences, New York University, Chair, SIAM Board of Trustees, Scientific Advisory Board, Fields Institute of Mathematical Sciences, Board of Directors, Canadian Mathematical Society

BIRS kindly invited me as an outside speaker in the Pacific Northwest Numerical Analysis Workshop, Sept 30-Oct 2, 2004. It was a great opportunity for me to catch up with the numerical analysis community in B.C. and Washington State, learn what others were doing, and talk about my own recent research. I graduated from UBC thirty years ago and have spent my career at the Courant Institute in New York, but I very much enjoy opportunities to return to Canada and make contacts with old and new friends. In this case, ``old" and ``new" are apt descriptors, as the most exciting part of my visit research-wise was an interchange with Jim Varah (just retired from UBC) and Chen Greif (a young faculty member there). Varah and Greif are interested in the question of how to optimize the condition number of a low-rank perturbation to a singular or nearly singular matrix, an interesting question mathematically that also has important potential applications. This optimization problem is nonconvex but amenable to some numerical techniques that I have been working on recently. We made some interesting observations just running MATLAB on my laptop at BIRS, and since then Varah and Greif have apparently obtained some beautiful theoretical results that I haven't yet absorbed. In any case, it was a fascinating problem and a delightful place to work on it. The setting at BIRS is really spectacular and there is absolutely no doubt that the availability of such a facility has enormously improved the Canadian mathematical infrastructure. A place like BIRS attracts top people from all over the world who would not be interested in attending a conference in an ordinary big-hotel big-city location. The peaceful atmosphere is very conducive to conducting research as it affords the opportunity to concentrate and to interact with others in an informal surrounding. The quality of the workshops at BIRS is also outstanding. There is so much interest in BIRS that the workshop selections process is very competitive (as I know since I was hopeful to attend another one that ultimately wasn't funded, not because the quality wasn't high, but because of the limited number of slots).

You are very fortunate to have a facility like BIRS, and I look forward to another productive visit on another occasion.

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Vilmos Totik, professor of mathematics, USF and U. Szeged, Member of the Hungarian Academy of Sciences

I have been participating at a workshop on pluripotential theory. This is a relatively new and fast growing subject, and BIRS made it possible to gather experts and to-be experts from all over the World. It was a really stimulating experience to listen to the talks and making contacts with people working in other areas. The BIRS facilities were just outstanding, I believe we need an Oberwolfach like BIRS here in Canada and the US. It was particularly appealing that BIRS was supporting new areas such as pluripotential theory.

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Priscilla Greenwood, Research Professor, Department of Mathematics and Statistics, Arizona State University

I participated in a BIRS workshop in August 2004. It was on the topic of stochastic models in genomics. Genomics has become a ``hot" topic lately, particularly certain highly statistical aspects. This workshop was distinguished by having a different focus, and by bringing together top probabilists several of whom are working in this area only recently, as well as some very outstanding well-known geneticists, and several young people who are being drawn to the fascinating new field of stochastic modeling in genomics. My own work in this area is not published yet ( not many people know I am doing these things) and so this workshop was an excellent way for me and others in my position to participate, find out who else is involved and what range of things are happening. I learned, for example, that a colleague at the University of Frankfurt, Anton Wakobinger, with whom I had been out of touch for several years, is now working on topics very close to mine. We are now in touch about our common interests.

As a joint U.S.-Canadian citizen and long-time faculty member at U.B.C., now working in the U.S. because of B.C. retirement rules, I am proud to have the first ``Oberwolfach-like" mathematical meeting place in North America located at Banff. This gives Canadian mathematical sciences a new prominence in the world, and contributes importantly to bringing the mathematical world to Canada.

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Lorenzo Sadun, Professor of Mathematics, University of Texas at Austin

I have been to two week-long BIRS conferences (Joint dynamics in 2003 and Aperiodic Order in 2004) and am helping to organize a Focussed Research Group in Topological Methods for Aperiodic Tilings in 2005. The two past conferences were excellent, and greatly helped my research. I can only hope that this summer's FRG will be up to the same standards!

At the 2003 Joint Dynamics conference, Robbie Robinson posed an interesting problem in one of his talks. Hiking on Tunnel Mountain the next day, Charles Radin, Charles Holton and I solved it. I also received very valuable feedback on the work I was doing with Alex Clark on deformations of tilings. With the help of that feedback, we solved the problem completely several months later. I also learned a tremendous amount about the interaction of C* algebras and tiling theory.

Although the 2004 Aperiodic Order conference has not (yet) yielded such dramatic successes, it has greatly influenced my work this year, and the work of my graduate student, Betsygail Rand. Discussions I had with Ian Putnam on pattern-equivariant cohomology led directly to Ms. Rand's PhD thesis problem, on understanding this cohomology in a rotationally equivariant way.

In my experience, BIRS is clearly succeeding in its mission to facilitate high-quality mathematics and high-quality mathematical interactions.

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Rebecca Tyson, Assistant Professor, Department of Mathematics and Statistics, Okanagan University College

I hasten to write this email with my full and enthusiastic support for the BIRS workshops. I have attended two such workshops, one in the summer of 2003 (The Legacy of Lee Segel) and one which has just ended (Mathematical Models for Biological Invasions). Both BIRS workshops have been incredibly useful experiences for me in terms of my research career, for a number of reasons.

At both workshops I had the opportunity to meet with a large number of important researchers in my field, and to discuss my research with them. I made some contacts which have remained extremely important to me throughout the following year, and I anticipate that these friendships will continue to grow and provide valuable support to my research program in a number of ways. These can include direct collaboration, but contacts can also be sources of graduate students and postdoctoral associates, invitations to conferences, invitations to seminar series, and co-organisers of workshops and meetings.

My own research program has had time to grow since my first BIRS workshop, and so at this most recent one I have made no less than four research contacts which may shortly lead to collaborative work which I couldn't otherwise have done. I have also benefited from the impressive knowledge of the assembled group, and am anxious to apply the ideas and techniques I have gained to my current research problems. As at the first workshop, I have also considerably expanded my network of research contacts, and I am certain that these will be equally important to my research activities as the contacts I made in July 2003.

All of the benefits listed above can be obtained at a conference, but never with the same magnitude. BIRS workshops are unique in that they gather a small group of people together for an intense scientific interaction over a period of several days. Even meals are taken together since everyone is housed in the same place. As a result, friendships are much more easily formed, it is not difficult to meet everyone on a more than superficial basis, and collaborations are easy to initiate. There are the time and the opportunity to talk science with co-participants, and the atmosphere is unhurried, pleasant and conducive to productive research.

I was absolutely delighted to be invited to my first BIRS workshop. When I received my invitation to a second one I felt as though I had won the lottery! I can't recommend these workshops highly enough, and I hope that they continue for some time to come.

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Juan Migliore, University of Notre Dame

I was fortunate enough to participate in the workshop ``Commutative Algebra and Geometry," held at the Banff International Research Station from March 29 to April 3, 2003. The organizers were Mark Green and Jurgen Herzog. It was a very stimulating experience for me. It brought me in contact with many other researchers in my field, and a lively and useful series of conversations took place. Some of these contacts are people that I have seen only a few times, or indeed in one or two cases people I had heard of but never met. In particular, speaking with David Cox allowed me to make improvements to a paper that was nearly finished (joint with Chris Peterson), that has since appeared in the Journal of Symbolic Computation. Speaking with Mircea Mustata provided useful insights (about what was and was not known) that guided me in a joint paper completed later with Rosa Miro-Roig and Uwe Nagel, that has since been accepted by the Journal of Algebra. I also had useful conversations with Aldo Conca, Tony Iarrobino, David Eisenbud, Mats Boij, Martin Kreuzer and Greg Smith. And several of the talks were very interesting to me.

BIRS is in a wonderful location, and is set up in a way that is ideal for mathematical research. It compares very favorably with Oberwolfach, in Germany. I am very happy to have attended this workshop, and my research has certainly benefited from it. Thank you for the fantastic service that your Institute provides for the mathematical community.

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Mengzhe Maggie Wang, Department of Math and Stat Sciences, University of Alberta

I like BIRS in Banff. It helps me a lot in my research. Also I enjoy the beauty there.

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Cliff Burgress, Perimeter Institute for Theoretical Physics, Department of Physics, McGill University

Hi, i had a good experience which i can relate.

I attended the BIRS workshop on string cosmology in June 2004, which was a very good meeting. At this meeting my collaborator, Fernando Quevedo from Cambridge University, was also present and we spoke about our work wherein we were able to find a particularly simple example of inflation within string theory, which we came to call ``Racetrack" inflation. Andrei Linde and Renata Kallosh, from Stanford, were there and did not believe our solution was possible. (This was rather daunting because Andrei Linde is one of the inventors of inflation, and so has considerable experience with it.) They were skeptical because they'd tried themselves to do the same thing, and had not been successful. After lengthy discussions we were able to sit down in the BIRS kitchen with our laptops, and explicitly verify our solution to everyone's satisfaction. They then joined us, adding many valuable ideas, and we wrote a paper about this mechanism shortly thereafter. (the reference is JHEP 0411:063,2004 e-Print Archive: hep-th/0406230)

This is an example where the resolution of the disagreement was only possible because we were all together in an environment which was conducive for doing so. And this has been a very fruitful collaboration which only happened because of this exchange.

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Pengfei Guan, McGill University

I am writing to support the continuation of funding for BIRS. BIRS is one of the best place to mathematicians together for exchanging of ideas in very front of mathematical research. It is a unique such setting in North America, it benefits the mathematical community in whole. I participated two BIRS workshops and organized one in past two years. It's great experience for me and for most of the participants of these two workshops. Neil Trudinger mentioned to me after a BIRS workshop to me that it's the most stimulating workshop he ever attended.

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Bill Johnson, Department of Mathematics, Texas A&M University

BIRS is a fantastic resource and I hope that your application for renewal is successful.

It was useful for me to see at BIRS the great activity of the young researchers in convex geometry. The focus of my own research has shifted, but attending that one workshop brought me up to date on what is going on in convexity. This has help my direction of two current graduate students, one of whom is investigating a direction discussed at the BIRS workshop I attended.

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Peter Russell, Department of Mathematics, McGill University

It is a pleasure to respond to your letter and heap some well deserved praise on BIRS. I came to Banff twice, first for a very successful five day workshop in the spring of 2003, and then this summer for the rather unique experience of participating in three weeks of focused research that brought together two researchers from Japan (Miyanishi, Masuda), one from India (Gurjar) and myself from Canada. We had prepared our meeting well, getting together beforehand in varying combinations at Osaka, Mumbai and Montreal, but it took the time in Banff and BIRS' congenial facilities, with all four of us away from the distractions of a home institution, to bring out the full power and pleasure that a period of intensive collaboration among exerts can provide. Our joint investigations raised as many questions as answers, and they are by no means finished, but a substantial manuscript coming out of them already is in the final stages of preparation. I doubt this work could now be at the stage it is without the opportunities provided by the research in teams program at BIRS. I am much looking forward to another opportunity to spend time at BIRS. With best wishes

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William McGowen Priestley, Professor of Mathematics, University of the South

I participated in a BIRS seminar in creative writing in the sciences that was held in April, 2004, and found it to be a wonderful experience.

At the time of the seminar I had completed the first draft of a paper entitled ``Plato and Analysis", in which I considered the extent to which Plato might have been affected by Eudoxus' brilliant use of number to account for proportions in which ratios of incommensurable magnitudes may appear. Because the connection between Eudoxus' theory and Richard Dedekind's nineteenth-century theory of real numbers is well known, my paper has the effect of connecting some of Plato's ideas to those of nineteenth-century analysis. ``Plato and Analysis" has since been accepted for publication by the Mathematical Intelligencer and should appear soon.

The comments about my first draft made by other participants in the seminar were of great help. In particular, I made the acquaintance of Jan Zwicky, who teaches Plato in Victoria and who furnished a valuable reference to me, making a connection between my topic and Plato's enigmatic ``last lecture" on the Good. This was a surprising and valuable connection that I had not foreseen.

Chandler Davis, one of the co-organizers of the seminar, also gave me much sound advice and encouragement.

Another topic, that of mathematics and poetry, is one in which I am interested as an amateur, and on another occasion during our seminar I participated in an informative discussion about this. Having to prepare something to say about this topic to a group so knowledgeable in this area was a real challenge and a rewarding experience. It is possible that this might lead to another paper down the road.

I worked hard, I got a lot done at BIRS, and I enjoyed having my wife Mary, who is a botanist, accompany me. It was our third time to visit Banff, although our first at BIRS. We love Canada.

I am very grateful to BIRS for inviting me to such a beautiful and hospitable place.

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Rene Carmona, Paul M. Wythes '55 Professor of Engineering and Finance Bendheim Center for Finance ORFE, Princeton University

I participated in two workshops organized at the Banff Research Center. I accepted the first invitation because the workshop was to celebrate the retirement of a good old friend (John Walsh) for whom I have a great admiration. I discovered Banff and the Research Station on that occasion. I was very impressed by the working conditions, the hospitality of the organizers, the stunning view, the beautiful weather (I understand this is not part of the package, but that was icing on the cake in that instance) and the SURREAL food. I am a gourmet snob, and I was amazed by the number of options and the quality of most of them. In terms of lodging, The accommodation is much better than what is offered in most math centers I have been, and except may be for the fact that I had to share a bathroom (some things become more difficult when we reach a certain age!!!) I was very happy with the living conditions. My only complain is the fact that Saturdays and Sundays are some of the most busy days in the workshop line-ups. I had to miss a couple of the talks I would have loved to hear, just because I do not want to go to conferences on these days.

But short of this minor inconvenience, my experience was very positive and I could not wait to be invited back. So I immediately accepted the invitation to participate in the math - finance workshop last June. And again, the local organizer was extremely nice and accommodating, the workshop ran smoothly, the afternoon hike was memorable, ..... I got all the perks I expected. On the scientific side, the level of the conference was also of the highest level and ALL the talks were of high caliber: I did not miss any. The atmosphere at Banff is very relaxed and very conducive to discussion. I do not know if it is as easy in the winter, but I had ample opportunity to spend time with colleagues discussing research problems in informal settings at different times of the day, in different settings.

If I were in your shoes, I would not worry about people like me. I would be more concerned about the young participants. Do they have enough opportunity to interact with the speakers and the leaders in the field. Is the fact that the times of lunches and dinners are loose, and the fact that they are taken in a very large dinning room shared with many other groups a hindrance making it more difficult for young (potentially shy) people to mingle with the more senior (less inhibited) fellows. I did not have any problem, and I found the atmosphere of the dinning room very inviting. But did they?

The Banff Research Center is a good thing for the math community, and I am glad that it is in good hands.

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Krzysztof Burdzy, Department of Mathematics, University of Washington

My participation in a conference at BIRS was a great opportunity for me to meet senior colleagues and junior mathematicians. I discussed mathematics with many of them and one result and one forthcoming paper have roots in these discussions. I talked with others about my own research and about problems that they presented in talks. BIRS offers incredibly good living conditions, with comfortable rooms and fast Internet access, and natural places to meet. The beauty of the surrounding mountains encourages walks, and these present an opportunity for informal discussions of professional matters. I hope very much that BIRS will continue its activities. It has an unquestionably positive and real impact on research of scientists who are able to participate in BIRS workshops.

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James Propp, Mathematics Department, University of Wisconsin-Madison

The workshop on discrete probability that I attended in summer 2004 was a huge boost to my research on rotor-routers. Preparing a talk on the subject helped me sharpen my focus and identify good points of attack, and having Ander Holroyd around to collaborate with enabled me to solve some simple problems and develop basic techniques. Also, Yuval Peres helped me realize that rotor-routers aren't a mere curiosity (as I'd thought) but potentially part of a toolkit for derandomizing many discrete stochastic processes. I've recently written a grant-proposal to spend three years working out the details, and I am fairly confident of NSF giving me the funding I've requested; in any case, the proposal I submitted wouldn't have been nearly as well-developed or compelling if I hadn't participated in the BIRS workshop and benefited from the breadth of knowledge of colleagues and their technical assistance and friendly encouragement.

I should add that the backdrop of Banff is an integral part of the spur to creativity that the Centre provides. Much of the hard thinking that took place during my two weeks at BIRS took place while Ander and I were hiking, or while I was sitting on the banks of a lake, playing with some physical embodiments of rotors. The countryside surrounding Banff is a resource that no other research center in North America offers, and is part of what makes Banff such a special place.

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Yasha Eliashberg, Department of Mathematics, Stanford University

I participated in, and even co-organized, a ``hot topic" BIRS conference on Floer homology for $3$-manifolds in November 2003. I think everybody, me including, liked very much the format of the conference, the setting and the way it was organized by BIRS' staff. The conference was very successful mathematically. As a result of the interaction during the conference a serious breakthrough in 3-dimensional topology had happen. What is important that it was not just a result of a progress in one of the participants' work, but it was a combination of small steps done by several people who otherwise do not regularly interact. I mean the development which led to the proof of Property P by Kronheimer-Mrowka and a conjecture of Milnor proved by Ozsvath-Szabo. I am happy that was able to contributed a small but essential brick to this building. I think that BIRS center is doing a very important job, which, I hope will successfully continue and develop.

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Rene Schoof, Universiteit van Amsterdam

I had a wonderful stay at BIRS. The scientific level of the conference (on explicit number theory) was good and the organization of was very professional.

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Neal Madras, FRSC, Chair, Department of Mathematics and Statistics, York University

I have attended two BIRS workshops: a 5-day workshop on mathematics of polymers in May 03, and a 2-day meeting of Chairs of Canadian Math Departments in Sept 03. Both were highly enjoyable. The 5-day workshop was particularly stimulating, one of the best I have ever attended. There was a concentration of people working on topics that I had been working on (self-avoiding walks and related polymer models), which does not happen very often. There were also others working on related topics (e.g. knots in random polymers) which I had heard about elsewhere, but it was really at this meeting that I got a deeper understanding of the issues and relevance of these problems.

Although I was not an organizer, it is clear that having the BIRS structure in place allows the organizers to focus on the scientific content of the meeting rather than its organizational details. As an organizer of meetings at York, I can appreciate this tremendously.

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Oliver Brock, Assistant Professor, Department of Computer Science, University of Massachusetts Amherst

I attended a workshop on the flexibility of proteins at BIRS this summer. This workshop was a truly enlightening experience. Problems in molecular biology are inherently inter-disciplinary and to gain true understanding requires knowledge biology, physics, chemistry, geometry, computer science. To make progress in such an interdisciplinary area, collaborations across departmental boundaries are absolutely essential. The workshop at BIRS created the opportunity to engage in such collaborations. I feel that BIRS plays and will continue to play an essential catalytic role in research in North America that cannot be otherwise fulfilled.

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Lionel Mason, Reader in Mathematics, University of Oxford

I would like to say that the meeting that I attended in PIMS at the beginning of August on Conformal Geometry was extremely stimulating and has subsequently led to some important collaborations and new ideas in my research. I very much enjoyed the fertile environment and atmosphere and the seamless organisation that made this such a productive meeting for me.

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Ian Agol, University of Illinois at Chicago

I participated in the BIRS workshop on low-dimensional topology in September 2003. Besides having some good talks which informed me of current topics that others are thinking about, a collaboration has ensued stemming from the talk I gave. I discussed some monotonicity formulae for the Ricci flow, and how this gave improved lower bounds on the volumes of hyperbolic 3-manifolds. Nathan Dunfield was at my talk, and after the meeting, he investigated my approach and found some improvements to get even better lower bounds. We will write a joint paper, but we aren't planning on submitting it until Perelman's work on geometrization has been checked to be fully correct, since the bounds depend strongly on Perelman's work. Also, we could check our volume estimates against data from the program Snappea, giving further validation to Perelman's work.

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Jesse Barlow, Department of Computer science and Engineering, Pennsylvania State University

I spent one week at the Banff Center last year during the week of the American Thanksgiving. It was for a workshop on eigenvalue computation. I can honestly say that it was one of the most enjoyable professional weeks I have ever spent. I dearly hope that I am invited to spend such a week again in the near future.

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Paul Gunnells, Mathematics Department, University of Massachusetts

I have participated in two BIRS Workshops:

(1) The many aspects of Mahler's measure, held April 26 - May 1, 2003 (2) Explicit methods in number theory, held November 13 - 18, 2004.

In both cases I found the workshops to be extremely stimulating, and highly informative. The facilities at BIRS were also excellent; with all our needs taken care of (food and lodging), there was ample time to discuss mathematics and interact socially with colleagues.

Both BIRS conferences had a significant impact on my own research. The Mahler conference introduced me to a branch of number theory I only knew a little about, and gave me a chance to meet many new colleagues. The Explicit methods conference gave me a chance to hear of many recent developments in number theory. Perhaps the most concrete way that BIRS has affected my research is a publication that grew out of interactions at the Mahler conference, namely Lattice polytopes, Hecke operators, and the Ehrhart polynomial available at the mathematics archive:

http://arxiv.org/abs/math.CO/0405573

BIRS is gratefully acknowledged in the introduction.

I would really like to see BIRS expand its operation from 40 to 48 weeks during the year. The setting is ideal for mathematics conferences, and I look forward to attending and perhaps organizing BIRS workshops in the future.

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Eric Cytrynbaum, Assistant Professor, Department of Mathematics, University of British Columbia

I was fortunate enough to be invited to one of the BIRS workshops last year (in honour of Lee Segel) and will be co-organizing one this coming summer with a few colleagues (on modeling in cell biology) and have the highest praise for the organization and venue. The meeting I attended was excellent both scientifically and in the ``mundane" details - good accommodations and food, helpful staff - and ranks among the most enjoyable and fruitful meetings I attend (for example, I would compare it quite favourably to the Gordon Research Conferences I've attended). I am really looking forward to the meeting we are organizing this summer as it will be drawing an international crowd of experts from a wide range of fields offering a great opportunity for building interdisciplinary collaborations, a vital component of my (and many of the attendees') research. I am certainly glad that we have such a valuable resource available to us and have no doubt that our meeting this summer will reflect favourably, in the minds of our international attendees, on the research and research environment here in Canada.

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Nora Ganter, Department of mathematics, Massachusetts Institute of Technology

I went to two workshops in Banff during the last 1 & 1/2 years: One was on ``Intergration on arc spaces, elliptic genus and chiral de Rham comlex".

It gave me the opportunity to meet mathematicians with backgrounds that are very different from mine who are interested in the same field as I am, but for very different reasons and with very different points of view. I have kept in touch with many people whom I met for the first time in Banff, one has since become a collaborator.

The other conference I went to was on ``Topology of manifolds and homotopy theory".

This conference, too, was a great conference and a good opportunity for scientific exchange with colleagues. Again I was able to make new contacts and to deepen existing ones.

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John Labute, McGill University

I participated in a Research in Teams (Field Theory and Cohomology of Groups) at BIRS in May 2003 with Jan Minac and Dikran Karagueuzian. This was a marvellous experience with me as it opened up a whole new area of research for me but one which built on my previous experience. In addition, it started a fruitful collaboration with Jan Minac which has already yield interesting results in Galois Cohomology with more to come. The facilities at BIRS were just marvellous and very conducive for serious work. I hope to be able repeat the experience in the near future.

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Dagan Karp, Department of Mathematics, University of British Columbia

BIRS has had a significant impact on my PhD thesis and current research program. At BIRS, I had valuable discussions with individuals that I would otherwise have not met. Those discussions opened new avenues for research and collaboration.

Let me elaborate. I was a participant at the Interaction of Gromov-Witten and Finite Type Invariants workshop in the fall of 2003. This workshop was also attended by Chiu-Chu Liu of Harvard University and Marcus Marino of CERN. Through discussions, we learned that my PhD thesis in Gromov-Witten theory was related in an unexpected way to the theory of the so called topological vertex of Marino and his co-authors. The vertex was a physical theory, and Liu was in the process of developing a mathematical theory of the topological vertex.

In detail, in my thesis I compute the local Gromov-Witten invariants of configurations of rational curves in a Calabi-Yau threefold. These same invariants are conjecturally computed by the technology of the topological vertex, how ever it is not a priori clear how to do so.

My results raise interesting questions about the topological vertex, and the relationship between Gromov-Witten and Chern-Simons invariants that it encodes. Indeed, my current research involves trying to understand how the topological vertex accounts for the pattern shown in my thesis.

In light of this, it is not an overstatement to say that my involvement at BIRS has been central lead to developments which are central to my current research.

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David Boyd, Department of Mathematics, University of British Columbia

I'm pleased to give a testimonial to the effectiveness of BIRS. I organized a BIRS workshop on Mahler's measure in April 2003 and I have just participated in another on Explicit methods in Number Theory in November 2004.

The Mahler measure workshop was very inspiring to my research. Vincent Maillot gave a lecture on generalizations of Deninger's cohomological interpretation of Mahler's measure. Inspired by this, my collaborator Fernando Rodriguez Villegas was able to make some conjectures about the values of some simple 4 and 5 dimensional Mahler measures, relating them to values at integers of certain modular forms. These results have been verified numerically to high accuracy but still remain conjectures. Following this up, he and I found a number of examples of 3 variable polynomials whose values we predicted should be expressible in terms of L-functions of elliptic curves evaluated at s = 3. These too have been verified to high accuracy and are challenging conjectures for future proof.

In the course of this, I found a three variable polynomial for which the elliptic curve of the previous examples degenerated to a rational curve, and so I predicted that the Mahler measure would be a rational multiple of $\zeta (3)\over \pi^2$, where $\zeta$ is the Riemann zeta function. Numerical evaluation (not an easy calculation!) revealed that the rational number was 28/5 to 28 decimal places. This conjecture was proved by John Condon, a student of Fernando, and formed a major part of his PhD thesis. My own student Mat Rogers has recently simplified the argument by proving some new polylogarithm formulae of considerable interest. This seems likely to be the inspiration for his own PhD thesis.

So clearly this workshop generated a considerable amount of interesting research just from my own local perspective.

It is a bit too early to see what the salutary effects of the November workshop will be, but it has got me thinking about some interesting questions. There were some very inspiring talks especially by some of the young Dutch algebraic geometers.

The atmosphere of BIRS, both physical and intellectual is very conducive to opening up ones mind to new ideas. It was a great idea to start the Institute. I think it will have an extremely positive influence on the future of Canadian mathematics.

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Xiaolin Li, AMS Department, SUNY at Stony Brook

Last year's workshop on moving interface problems is of great help to our research program. From this conference, we learnt how the level set people have tested their method on accuracy and reversibility of the moving interface. After coming back, we did the same test problem on the front tracking method. When we used the fourth order Runge-Kutta method, the front tracking showed much accurate result than the level set method.

We also learnt that the success of the level set method was due to its simplicity, but simplicity can be achieved through design of a easy code interface. This has been the work I have initiated after the Banff workshop.

The workshop was compact and interactive. I made very good friend and close contact with the people in the same field. It is a unforgettable academic experience.

By the way, our family also enjoyed a beautiful vacation after the conference. My son took many spectacular photos in the Canadian Rockies.

Thanks for the organizers and the invitation.

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Uri Ascher, Department of Computer Science, University of British Columbia

I participated in a meeting on model reduction and numerical linear algebra last April and in a regional weekend-size meeting of numerical analysts this past September. Both meetings were highly successful, and I credit the BIRS operation for its high standards and efficiently run, first rate facilities. The meeting last April gave me the opportunity to learn a lot about an important area, model reduction, as well as interact with several colleagues on research questions related to linear algebra that arise in my work (I apply such techniques rather than center my research on them).

The regional meeting was by far the best PNWNAS meeting I have ever attended (and I have attended many). It seemed, I confess to my surprise, that my colleagues needed that extra time and remoteness of location to come out of their daily toils and share their interesting research projects in a more meaningful way.

I strongly support the continuation of funding for the BIRS facility. It clearly contributes a lot to the mathematical sciences scene in this country.

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Michael Chen, IE Dept, Tech C230, Northwestern University

I attended the 6th PIMS Graduate student Math Camp at the Banff International Research Station in 2003. It was a very memorable experience. Our team worked on two industrial problems and gave satisfactory solutions. I made friends with my team members and they provided helps from time to time on my study and research.

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Atul Narang, Chemical Engineering Department, University of Florida

I attended the BIRS workshop ``Dynamics, control and computation in biochemical networks" held in August, 2003. It was by far the best workshop I have attended so far. Since I am modeler, it was particularly helpful to have a large number of experimentalists in the audience. Their input has been crucial in the subsequent direction of my work.

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James Sethian, Professor of Mathematics, Department of Mathematics, University of California-Berkeley, Head, Mathematics Department, Lawrence Berkeley National Laboratory

I attended the BANFF workshop on Numerical Algorithms for Propagating Interfaces--August 2003. I've been to many workshops in this area over the years, but this one stands out: (1) The organizers did a wonderful job of selecting a wide range of techniques, applications, and speakers. The conference was free of the highly opinionated talks, and the focus was focussed on cooperation and the underlying mathematics. (2) I began conversations with two of the researchers whom I had not met before: perhaps these will come to fruition. (3) The large amount of time devoted to the talks, the free parts of the schedule where people could truly interact, made this unique.

This was a success.

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Anand Pillay, Department of Mathematics, University of Illinois at Urbana

I found the March meeting at BIRS on model theory (which I was formally an organiser of) very enjoyable and also very useful. I managed (with collaborators who were at the meeting) to finish off the proof of a result we wanted, stimulated by various comments during the lectures.

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Wayne Barrett, Department of Mathematics, Brigham Young University

I attended the BIRS workshop ``Directions in Combinatorial Matrix Theory", which was held May 6-8, 2004. The following week I wrote to my colleague Richard Brualdi, ``For me the Banff conference was exceptional."

Besides hearing a dozen clear and very informative talks over the 1 1/2 day period, the conference contributed indirectly to the following publication:

Wayne Barrett, Hein van der Holst and Raphael Loewy, Graphs whose minimal rank is two, The Electronic journal of Linear Algebra, volume 11 (2004), pages 258-280.

The Monday after returning from the conference I sent a letter to the Editor of Journal of Combinatorial Theory B about a paper that R. Loewy and I had submitted. The letter began:

We are writing to enquire about the status of our paper, Graphs whose Minimal Rank is Two (JCTB File: 5109). As you will recall, we first sent you an enquiry be e-mail on March 5, and asked if you would be willing to contact the referee in our behalf. You have been looking into this for us.

Raphael Loewy and I were invited to attend a workshop, Directions in Combinatorial Matrix Theory, at the Banff International Research Station in Alberta last week. We were somewhat surprised that three of the speakers gave talks on the minimal rank of a class of matrices associated with a graph, and two others mentioned such problems; one of these explicitly mentioned our work, and others referred to it. This has made us even more anxious to reach a final resolution on the disposition of our paper.

The outcome of this letter was that on the following day we received from the Editor the name of the referee, Hein van der Holst, with whom we had never before corresponded. We collaborated by e-mail over a six month period and added many substantial results to the already existing paper; it was published electronically in November. I believe this is one of the top 3 or 4 papers that I have ever written. And the three of us have written and submitted one further paper also.

This may have happened without the Banff workshop or it may not have. The workshop gave the impetus to write the follow-up letter which got everything rolling. I will always remember that with appreciation.

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Fei Xu, Associate Professor of Psychology & Canada Research Chair, Department of Psychology, University of British Columbia

I participated in a workshop at the Banff International Research Station in March 2004 and it was one of the most productive and inspiring professional experiences of my career. I arrived at the University of British Columbia as an associate professor of psychology in 2003, then I was invited to Banff for a workshop organized by Janet Werker and colleagues. We spent two days discussing statistical learning in infants and adults and issues on learning language in general. Banff provided an ideal environment for such intense workshop. The participants not only attended each other's talks but also many breakfast/lunch/dinner discussions which are lengthy and details, going much beyond a regular conference gathering. As a result of participating in this workshop, I have begun some research on learning in infancy in my laboratory at UBC. There is absolutely no doubt in my mind that the Banff International Research Station is a major locale for extremely productive workshops, conferences, and the development of international collaborations.

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Congming Li, Department of Applied Math, University of Colorado

My experience at Banff was great.

The most beneficial part is the discussion with other researchers and fund mutual interest to work on problems. The setting gives us a lot of discussion time which is the greatest part of my Banff experience. I have started 2 research projects there and one is already bearing some interesting results. Banff is a place I wouldn't want to miss: I will go whenever invited.

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Bernhard Lani-Wayda, Department of Mathematics, Justus-Liebig-Universitat Giessen

Visiting BIRS was an extremely pleasant experience for all participants. I cannot claim a direct connection between the conference and something as concrete as a subsequent research paper.

During the conference there were discussions on how to support the world-wide reputation of our area of interest (delay equations). This reputation is suffering partially from a lack of tradition, and partially from mass production of low-level papers.

The familiar atmosphere of the BIRS meeting supported very much the concrete manifestation of the collective will to improve this situation. In this context I was invited by Prof. Shui-Nee Chow (Georgia Institute of Technology, Atlanta) to a conference in Taiwan 2005, with the specific aim to present substantial mathematics from our field.

We all strongly hope that BIRS will continue its so far extremely positive development.

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Mark L. Green, Director, Institute for Pure and Applied Mathematics

I was an organizer for a workshop at BIRS on Commutative Algebra, and also attended the workshop, staying around for a few more days to do some research in teams. Speaking as an institute director, I was very impressed with the BIRS operation-the facilities, the staff, the ease of email, the room for informal get-togethers, and the pleasantness of the lodging. Speaking as an organizer, things were made pretty easy for us, we received timely reminders of tasks that needed to be done, and were relieved of responsibility for the material organizaton of the workshop. Speaking as a participant, I found the experience quite valuable and my ``team" did indeed make substantial progress on our project, which is in the process of being written up.

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German Enciso, Rutgers, The State University of New Jersey

As a speaker of a conference at Banff this past August, I would be very happy to be able to contribute to your petition by describing my experience at the station. I don't know how to say this and sound honest at the same time, but it was one of the very best times I have had at a conference. This particular one (on quantitative biology) was very well organized and the talks were remarkably well prepared, but I have no doubt that the venue was key to its success.

The stunning surroundings and the excellent amenities gave many opportunities to talk to other people and start collaborations. I for one got to meet Leon Glass from Montreal, as well as a number of professors and postdocs from the US, and after the seminar I started a collaboration with Mattheu Louis at Rockefeller University.

I especially liked the fact that there were so many artists around: we got to talk for dinner and lunch many times together, and they provided a good contrast that brought us back to earth when the conversation was rather too technical (I believe that they enjoyed talking with us as well). The food by the way deserves a special mention: we commented back then that the restaurant gave the pleasure of being in an elegant restaurant, without any of the hassle for formality or the guilt.

I think that you have a beautiful country, and that you are doing a very good job of showing it. Thanks for the organization, I hope to have an opportunity to come back another time.

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Gary Walsh, Department of Mathematics, University of Ottawa

My research is in Diophantine Analysis. I recently attended the workshop on Analytic Number Theory and Diophantine Approximation (Nov. 20-25, 2004).

This was an extraordinary experience, nothing that I have experienced before, as I have not had the opportunity to accept invitations to Oberwolfach due to conflicts, and my closest experiences were at MSRI, which is a completely different environment.

This environment was SO productive. I was able to spend so much time with 3 colleagues on our joint research projects, but at the same time become very familiar with other ``hot" topics being pursued by others in my research (Diophantine Analysis) area, in order to get detailed insight into the methods being employed, and the hurdles that stand in the way of these approaches. Moreover, I was able to similarly learn the latest important ideas and discoveries in Analytic Number Theory, but for me, this aspect was secondary.

I sincerely hope that there are further BIRS workshops in my research area, and that BIRS is able to maintain the same productive format (a few, but not too many, lectures each day, leaving ample time for participants to pursue common goals, and exchange methods and research ideas).

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Thomas Coutelen,Department d'informatique et de recherche operationnalle, University of Montreal

First I want to thank you an all the MITACS organisation for the Banff workshop. It has been a great experience for me in several point of view: First, the variety of the subjects is a really good point in order to enlarge my point of view. The counter side may be that new collaboration may be harder to build. But this workshop was obviously oriented to security so that many collaboration probably born this week end. Then you gave me the opportunity to present my work for the first time so that I consider this experience as the beginning of my research career (I am still a MSc. student). I realize that day how hard I have to work in order to be believed and I realized how other topics may help me, even with subject quite far from my work.

At last if I was really impress to spend this time with so experienced people, everybody was respectful so that I have been charmed by this way of work.

To conclude, this experience made me aware that I really do want to continue to a research career what wasn't sure before.

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Luca Daniel, Massachusetts Institute of Technology

Participating at one of the BIRS workshops has had very practical repercussions on my research career and on the impact of my contributions in other communities different from mine (computer aided design) such as applied math and the system theory communities. As one of the many tangible testimonials let me send you for instance part of an email I just received a week ago (that is 8 months after the workshop).

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Leah Edelstein-Keshet, Department of Mathematics, University of British Columbia

It is with great pleasure and enthusiasm that I write to you to express my support for the Banff International Research Station (BIRS).

As you know, I was one of the co-organizers of a BIRS workshop in the summer of 2003 on Mathematical Biology, and the legacy of Lee Segel. This was one of the most wonderful scientific weeks in my entire research career. Let me explain why.

Our group of 40 consisted of a mixture of senior scientists who are at the pinnacle of this field (Simon Levin, George Oster, Alan Perelson, Gary Odell and others), together with bright young scientists, male and female, at the level of graduate students, post docs, and junior researchers. We attracted participation from international stars (Lee Segel, Paulien Hogeweg, Rob deBoer, Albert Godbeter, etc). The atmosphere was exceptionally pleasant, and days were spent in exciting talks, numerous informal discussion sessions at that were carried over to the dining hours, and which continued even outdoors. The level of scientific discussion was unparallelled! I saw an example of one research direction, involving the assumption of Glazier-Graner cellular Pott model that was dissected and shown to be incorrect from a Newtonian mechanics perspective. The discussion (which was intense and continued over two days) was carried out with the greatest respect and interest not as a hostile confrontation, but rather as a helpful revelation and deep interest in getting to the truth. This, alone, has changed the perspective of a number of young scientists working in the field of computational biology. There were several examples of this type. There were numerous examples of outstanding talks that were inspiring to us all. It is very rare to find scientific meetings in which such high caliber science is mixed so well with such congenial and intense interactions at all levels of seniority.

One reason for the high caliber of that meeting is the unique aspects of BIRS: the staff makes it easy for all of us to focus on science, rather than the administrative overhead of running the meeting. We had lots of help in advance of the meeting to finalize the list of participants and to get information and registration material sent to them. On site, every detail Everything we needed was right there, and we had help with all technical aspects. We were very impressed by the exceptionally good on-site staff, and how well they treated us. No request was ignored.

The second reason is that BIRS is optimally organized for such meetings. It is just the right size (maximum of 40 participants), with the right level of comfort, and the perfect environment. Unlike a meeting at a university campus, there are few distractions or interruptions, and the group is cohesive. This makes for very good atmosphere.

I had a second opportunity to spend time at BIRS at a MITACS biomedical theme meeting about 1 year ago. We took up a number of researchers from my MITACS team and had some prime research time. We could really concentrate on making rapid progress on a number of collaborative projects in the few days that we spent there.

I got so much from these experiences that I have proposed (with other co-organisers) another BIRS workshop (on Cell Motility and the Cytoskeleton) for the summer of 2005. This meeting was approved and I look forward with great anticipation to another unique and intense 5-day BIRS experience.

Finally, it goes without saying that the environment of Banff, and the geographical setting is both inspiring and uplifting: our group spent great hours discussing science on walks in the surrounding area. Needless to say, I am a strong supported of this gem, and I think that it will put Canadian science on the international map.

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Ezra Miller, School of Mathematics, University of Minnesota

I have attended two BIRS workshops:

1. Workshop 03w5005 on ``Commutative algebra and geometry", March 29 - April 4, 2003

and

2. Workshop 03w5009 on ``Recent advances in algebraic and enumerative combinatorics", May 3 - May 8, 2003.

For the first of these I was invited to give an hour-long talk on the topic of my choice. This presented me with a very timely opportunity. For a few years I had been working on an extended joint project with Allen Knutson (beginning with the paper `Gröbner geometry of Schubert polynomials', Annals of Math, to appear) and sometimes also Mark Shimozono (see my comments on workshop number 2, below). This work had been for some time recognized as relevant to certain communities of algebraic geometers and other communities of combinatorialists. However, although the work was strongly grounded in commutative algebra, it was not until my BIRS visit that I had an opportunity to deliver a relaxed, expository-style lecture to a concentrated group of leaders in commutative algebra. As far as I can tell, the talk went over quite well, and it had the desired effect of engaging the commutative algebra community in our research program. The exposure afforded by my opportunity at BIRS was very helpful for my career, especially given that I was just a couple of years past my Ph.D. at the time. For example, I think it would be fair to guess that my experience at the BIRS workshop 03w5005 was a major factor in precipitating an invitation to deliver a four-lecture series on combinatorial commutative algebra to a large audience of international researchers at the International Center for Theoretical Physics (ICTP, Trieste) in June, 2004.

During the week of the second workshop listed above, I was finishing up a paper with Allen Knutson and Mark Shimozono entitled ``Four positive formulae for type A quiver polynomials". The BIRS workshop 03w5009 was the FIRST TIME EVER that all three of us had been in the same room together. Our week at BIRS was therefore extremely valuable for that reason alone; but moreover, each of the three of us presented a part of the paper to the audience of distinguished combinatorialists there. We were able to announce, in full detail, the results, techniques, and ramifications of our substantial (by which I mean hefty: 76-page) article. We were also able to finish up the final bits of editing sufficiently to hand out preprints to interested audience members. The paper has since been submitted to Inventiones Math, and subsequent papers by other authors--of which there are at least half a dozen--include at least one that has appeared in the Journal of the American Math Society. A number of the ideas for this subsequent work were discussed during the workshop itself, and certainly the presence of all three authors facilitated these discussions.

Let me close by mentioning that the walks along the river and hikes into the mountains during both workshops were refreshing venues to mull over the mathematics being presented, and that after the May workshop, I spent a day skiing with a colleague in the vicinity of Banff--without question the best day of skiing I have ever experienced.

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James Demmel, Department of Electrical Engineering and Computer Sciences, University of California-Berkeley

Your request for a testimonial arrived at an opportune time. I helped co-organize the ``Theory and Numerics of Matrix Eigenvalue Problems" workshop from November 22 - 27, 2003. I'd like to mention one outcome in particular: I used the meeting to brainstorm with the other participants on what new eigenvalue algorithms were worth including in a potential new release of the widely used LAPACK and ScaLAPACK libraries. These libraries have been adopted by many computer and software vendors (Cray, IBM, HP, Intel, NEC, Mathworks (producers of Matlab), to name a few), and have 42 million web hits on their public web page, and so the impact of improving these libraries is large. Many of the participants had excellent suggestions (of their own and other algorithms). As a result, Jack Dongarra and I subsequently wrote a successful NSF proposal to get substantial funding to produce a new release of these libraries. Our first organizational meeting for the project is tomorrow, and I was planning it when your email arrived. In short, this BIRS workshop played a critical role in bringing together the leaders of the field to identify promising algorithms (including many which require further mathematical research to complete!) whose development and dissemination will have a very large benefit for a large fraction of the science and engineering community.

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Ernest Schimmerling, Department of Mathematical Sciences, Carnegie Mellon University

I participated in the BIRS meeting on ``singular cardinal combinatorics". It was one of the most exciting meetings that I have attended. I gave a talk about my results on ``coherent sequences and threads". John Steel pointed out an extension of one of my theorems. Stevo Todorcevic made useful suggestions for how to get started on some of the open questions I'd posed in my talk. (I'm still working on these!) I'm sure that the paper I'm writing will be better because of this interaction.

The Banff Center is an amazing place in terms of its beautiful location and great facilities, but particularly in terms of its friendly helpful staff and careful planning. I really appreciated their help when the airline lost my luggage. And I like the idea of mixing up groups at dinner. Besides working on research with mathematical colleagues, I had memorable conversations with non-mathematicians, including an Argentinian sound engineer who helps artists realize projects, and a British choreographer who was running a workshop for a dance company from Calgary.

Hopefully I'll get invited to future BIRS workshops. I'd jump at the chance!

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Stephanie van Willigenburg, Assistant Professor, University of British Columbia

I am writing to thank you for the opportunity to hold the 5 - day BIRS workshop on ``Combinatorial Hopf Algebras" from August 28th - September 2nd 2004.

Combinatorial Hopf algebras lie at the junction between a variety of disciplines. Aside from combinatorics and algebra, it also arises naturally in computer science, physics, topology and geometry. The BIRS workshop gave these disparate groups a rare opportunity to meet, to exposit on the state of the art in their fields and to formulate research programs.

I, myself, was able to meet computer scientists such as Robert Grossman and physicists such as Ale Frabetti, whose outlook on the subject gave me new ideas on how to approach problems I was working on. In addition, I also had the pleasure of meeting some of the pioneers of the subject such as Jean-Louis Loday and Pierre Cartier, who were drawn to the meeting by the exclusive list of participants.

Moreover, I was able to begin two new research projects: The Hopf algebra of graphs with Richard Ehrenborg, and The structure of ribbon Schur functions with Louis Billera. In the latter project, we found the computing facilities at BIRS to be invaluable for generating data, from which we were able to prove a theorem before the meeting's end.

I thank you again for the opportunity to research at this outstanding facility.

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Charles Radin, Professor of Mathematics, University of Texas at Austin

I understand that the Banff International Research Station is up for renewal. Since I have participated in two workshops - on Joint Dynamics in June 2003 and on Aperiodic Order in May 2004, and value the experience highly, I would like very much to support the application for renewal, at least with this note.

I have found the setting unusually conducive for research, both in the size and quality of the sets of participants, and in the physical facilities for formal presentation and for relaxed interchange. At the workshop on Joint Dynamics questions were raised which led to new results which I have submitted for publication - with acknowledgement to BIRS of course! And given this experience I will be an organizer of a workshop on Sphere Packing next May, and expect to participate in an FRG on Topological Methods next July. I certainly hope BIRS is renewed!

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Nadrian C. Seeman, Professor of Chemistry, Margaret and Herman Sokol Chair in Chemistry, Department of Chemistry, New York University

It is a little early to describe papers that resulted from a workshop held in August, but the workshop was influential in my thinking about a new project which we are undertaking in collaboration with one of the workshop participants, Erik Winfree. I realized during the workshop, and as a consequence of the talks that I attended, that we could use a translocational version of a rotary DNA translational device (we had already developed), to record the history of a system. We are now beginning to make the translocational device, and expect to fuel it with molecules from one of Erik's systems so that we can record the history in a series of polymers.

I hope this is help in pointing out the importance of the BIRS workshop's influence on my research.

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Barry Sanders, iCORE Professor of Quantum Information Science, University of Calgary

I participated in two workshops this year: a two-day workshop with the University of Alberta Theoretical Physics Institute and a five-day workshop on quantum computing. Both workshops were valuable for me. In the first workshop, I gave a talk and cemented a stronger relationship between my theoretical physics program at the University of Calgary and the spectrum of activities at the University of Alberta. I expect that this relationship will be formalized soon if, as expected, I will be made an affiliate of the University of Alberta's Institute for Theoretical Physics. The BIRS workshop was instrumental in establishing common interests.

The quantum computing workshop was quite valuable. It was focused on the mathematical and computer science aspects of quantum computing but afforded me with the opportunity to learn a lot from the speakers and from other participants who did not give talks. A postdoc in my group, Andrew Scott, had the opportunity to present our recent work and build an awareness of physics-related quantum information research to the audience of computer scientists and mathematicians, which helped them to appreciate our progress in quantum fingerprinting.

BIRS offers an important opportunity to meet and collaborate with mathematically-oriented researchers in a relaxed setting that is conducive to profound discourse. I certainly hope that BIRS continues, and I hope to participate in BIRS workshops in the years to come.

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Michel Waldschmidt, Institut de Mathmatiques Thorie des Nombres

I suppose it is better I write in English. Also if you wish a more formal letter please tell me.

I participated to a meeting in BIRS last week. That was my first visit to Banff, and it was an excellent experience. The main point for me is that I spoke with Damien Roy of my recent research, and he gave me an advice which hopefully will enable me to solve a problem on which I was working for several months. This is really important for my wok, and it would not have happened with our regular discussion by e-mail.

We had other discussions together, which were also very interesting for me, and the lectures which I attended were all of high level. The organizers had planned a rather light scientific program (14 lectures for 4 days) and that was a very good idea: we had enough time to work together (that was a workshop) and as I said this was quite efficient.

This participation of mine to this meeting may have further consequences later, but I cannot tell yet since it took place only last week.

I wish to add that at the CIRM (Luminy) we did not succeed yet to receive enough support for the accommodation of all participants. This is a good point for BIRS, which makes it very much attractive!

Thanks!

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Bob Guralnick, Professor of Mathematics, University of Southern California

I participated in the Galois Groups Workshop (the title may have been somewhat different, perhaps it was a focused research group) in September 2003. This was organized by David Harbater and Florian Pop. The setting and format with a small number of lecturers and lots of time to interact with the other participants was fantastic. The particular project that I was working on during that period was on lifting of automorphisms of curves from characteristic p to characteristic zero - this was a joint project with Harbater and Ted Chinburg (also a participant). Quite a lot of progress was made during the meeting. Moreover, several other participants made useful suggestions and pointed out useful items in the literature. Moreover, Bouw and Wewers (two other participants) have started working on a related problem and have produced some outstanding results.

BIRS is a wonderful resource for the general mathematical community and I think with the proper leadership and funding can take its place among the premier sites for mathematics (IAS, MSRI, Oberwolfach). It certainly is a great benefit to Canadian mathematics in particular.

It should be an easy decision to decide to continue supporting what is clearly growing into a wonderful institution.

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Yiming Long, Vice President of Chinese Mathematical Society, Nankai Institute of Mathematics, Nankai University

It is my great pleasure to write this letter to strongly support the further development of the Banff International Research Station for Mathematical Innovation and Discovery (BIRS). It is my great honor to have had been invited to give a lecture and join the workshop, New developments on variational methods and their applications hold during May 15-20 of 2004 at BIRS organized by Kung-Ching Chang (Peking University), Jingyi Chen (University of British Columbia), Changfeng Gui (University of Connecticut), and Paul Rabinowitz (University of Wisconsin, Madison). About 40 experts come from all over the world joined this conference so that it is at the highest academic standard in the world. Invited speakers include winner of the US Medal of Sciences, Professor Louise Nirenberg, Birkhoff Prize winner Professor Paul Rabinowitz, many other famous mathematicians, and also many young active mathematicians. Among the participants, about 1/3 are come from universities in Canada. In the conference I also reported a very recent work which push forwarded the study on a conjecture proposed by H. Seifert in 1948 about the existence of multiple brake orbits. This conference is very successful and provides an excellent opportunity for mathematicians to communicate face to face to discuss their commonly interested problems. Such an activity certainly is very important on pushing forward the research in mathematics. During my stay in Banff, I felt that the Banff center has a very nice facility for carrying out academic activities. For these reasons, I believe that such a research base is very important for advancing mathematics in the world and in the north America, specially in Canada. I would strongly support the further development of the BIRS and hope that BIRS will become one of the most active and important center of mathematics in the world.

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Justin Roberts, Department of Mathematics, University of California-San Diego

I attended the workshop on Gopakumar-Vafa invariants organised by Jim Bryan and Dave Auckly in November 2003. I thought this was an absolutely excellent meeting. The idea of bringing Marcos Marin o to speak about this new and exciting subject was a very good one, and I think it did a great service to the low-dimensional topology community to have a focussed workshop at which the ideas could be disseminated in this way. Personally I came to realise that this subject was very much related to what I had been thinking about for a long time, and it has influenced my subsequent work. It is very valuable indeed to have an ``Oberwolfach-style" centre in North America, operating these kinds of specialised meetings with selected invitees. They are in general much more useful than the normal sorts of conference at which there may or may not be much in common between participants.

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Ioannis Karatzas, Professor of Mathematics and Statistics, Columbia University

I am writing to express my very strong support for the proposal to renew the Banff International Research Station. This is an unparallelled facility for Mathematics, that can be compared only to the Oberwolfach Center in Germany. I had the good fortune to spend a week at the Banff Station during the summer of 2004, and recall very fondly the excellent organization of the meeting, the stimulating talks and informal discussions, the friendships that were made. I urge that the proposal for its renewal receive all the support you can command.

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Akshay Venkatesh, Department of Mathematics, Massachusetts Institute of Technology

I attended the BIRS workshop on ``Diophantine approximation and analytic number theory." This was a very exciting workshop for me that brought me up to date on some extremely interesting work by various groups in Europe with whom I was not in contact. Moreover, I had many extremely fruitful discussions with Paula Cohen, who explained many interesting questions connected to the Andre-Oort conjecture, at least some of which I think there is a chance of proving by ergodic methods. So it was an excellent conference; I also add that it provided an wonderful working environment, and I finished a paper with a co-author (also at the same conference) while there.

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Toby Walsh, University of New South Wales, National ICT Australia

The Banff International Research Station is a world class resource. I was invited to attend a workshop there in May 2003. The workshop was attended my many of the leading researchers internationally in my area of operations research and computer science. The discussions went on till late at night and provided valuable input to some of my recent publications. In addition, I made some very valuable new contacts at the workshop, one of whom I visited earlier this year to discuss a possible international collaboration. I therefore have no hesitation in congratulating BIRS for starting so well and strongly and vigorously support its continued funding.

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Eric Allender, Department of Computer Science, Rutgers University

I attended a BIRS workshop on Computational Complexity July 4-7, 2004. It was an excellent event; many of the top people in the field worldwide were in attendance, the facilities were very conducive to informal interaction, and there were lots of great lectures. Mike Saks and Toni Pitassi were also present, and our joint paper (together with Lisa Hellerstein) entitled ``On the Complexity of Finding Minimal Representations of Boolean Functions", grew largely out of discussions that we held there. (This paper is currently submitted for publication, it is available at my web page: http://www.cs.rutgers.edu/ allender/publications. I hope to have the opportunity to return to Banff for BIRS workshops again someday.

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Yang Wang, Professor and Associate Chair, School of Mathematics, Georgia Institute of Technology

I strongly support the renewal of BIRS. I had participated two BIRS workshops in the past two years, and each time I found it extremely stimulating. More than any other conference, you meet your peers on a very personal level, which has helped me to maintain very productive collaboration with some of the people I have met at BIRS. During the workshop time we had a lot of free time to interact, whether it is discussing mathematics or simply taking a walk in the town of Banff. Opportunities like this do not exist often. I would be a shame if BIRS is not able to continue.

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Klaus Mueller, Computer Science Department, Stony Brook University

I appreciate the BIRS effort very much. A similar effort (the only other one I know) exists in Germany with the Dagstuhl series. Although health reasons prevented me from coming to BIRS, when I was invited this year, I know that I find these kinds of gatherings of a select group of scientists extremely stimulating and beneficial to all. It is very different from a conference, where there is a usually a much broader intellectual mix of people and program composition. Meetings like BIRS enable participants to delve deeply into subject matters, fully exploring ind identifying the gist of the problems thanks to a debate among experts, whose different viewpoints and expertise provide the full picture needed to reach effective solutions. It's also great to build and deepen research connections useful for the future since the resort-like venue is very relaxing to all participants, eliminating the usual day-to-day schedule, stress, and routine. Going out, one feels as a part of a community.

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Shigeo Koshitani, Department of Mathematics, Chiba University

This is Shigeo Koshitani (Chiba University, Japan) writing, who took part in a workshop ``Current trends in representation theory of finite groups, October 25-30, 2003" taken place at the Banff International Research Station (BIRS).

First of all, let me confess that the workshop above was so successful and useful for my research in mathematics which is mainly on representation theory of finite groups. For instance, before I visited the BIRS, I had only a poor knowledge on representation theory of finite reductive groups and algebraic groups. However, at the workshop, I met several people who study on the area and who kindly introduced me many papers and nice books of the subject. Since then I have been trying to study it hard, and now I believe it works quite well.

Second of all, even in my major subject, which is on Broue's conjecture on representation theory of finite groups, I was informed many new informations and unpublished papers by other participants of the workshop at the BIRS. It has been helpful, of course, so much for my research, and because of them I could write a couple of papers on the subject which have been published or accepted already in a journal ``Journal of Algebra".

Moreover, I was able to become acquainted with several people during the workshop, and I actually visited one of them in Germany this year. This has given a so nice effect for my research.

Anyhow, I really appreciate that I was able to attend the workshop above, and therefore I am grateful to the BIRS so much.

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Sergei Gukov, Department of Physics, Harvard University

It is my pleasure to reply to this letter and acknowledge the hospitality of the Banff International Research Station. I had a great and productive time at the workshop ``Recent Developments in String Theory" in March 2003. The stimulating atmosphere of the workshop and the high level of scientific interaction make BIRS one of the best research stations in the World.

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Leslie Hogben, Department of Mathematics, Iowa State University

I wish to express my strong support for the Banff International Research Station (BIRS). I participated in the workshop Directions in Combinatorial Matrix Theory held there May 6-8, 2004. This was one of the best scientific gatherings I have ever attended. The talks were outstanding and open problem sessions were even better. The setting provided by BIRS is ideal, with all participants in the same building in a very pleasant setting, with time to visit informally as well as to attend presentations.

I have submitted a paper to the Electronic Journal of Linear Algebra, ``Spectral Graph Theory and the Inverse Eigenvalue Problem of a Graph," that is the result of my participation in this workshop. Some of the work was done in preparation for the workshop and the some as a result of issues raised there.

As a result of seeing relationships between some of the talks at the workshop, I organized a minisymposium, ``Spectral Properties of Families of Matrices described by Patterns or Graphs," to be held at the 12th meeting of the International Linear Algebra Society to be held in Regina, Canada in June 2005. This minisymposium features 7 speakers from Canada, Israel, the Netherlands, and the USA.

I now have two new possible collaborators, who will be making separate research visits to Iowa State (one next week and one in January). These visits are the direct result of the ability to chat with colleagues informally. Needless to say, I also used the time at BIRS to reconnect with colleagues I had worked with previously.

I sincerely hope that BIRS will continue to be able to offer such wonderful opportunities to mathematical researchers in the future.

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Qingguo Li, Simon Fraser University

It has been a great experience for me, and we have learned a lot from the workshop and summer camp.

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Pauline van den Driessche, University of Victoria

I have just returned from a workshop on Mathematical Models for Biological Invasions at BIRS. This workshop was a great success with discussion between mathematicians and quantitative biologists on current problems. As one of the organisers, I was very pleased with the depth of discussion and the number of contacts that were made at the workshop. Some participants said that it had given them a whole new dimension to their research, and I believe that collaborative papers will result from this workshop. In fact, participants generated a list of open questions to take home and work on. In the summer I helped to organise a summer school and workshop on mathematical epidemiology at BIRS. This proved very successful, and I know from comments of my two Master's students who attended that it really made a difference to their understanding of the subject. Also they worked in teams on projects, and this gave them a new and valuable experience. Our MITACS group was responsible for this summer school, and we had previously held a MITACS group weekend meeting at BIRS. At this meeting our group had some very valuable discussions and working sessions, and these have led to collaborative work on models for SARS and West Nile virus. One SARS paper by this group is recently published: A. Gumel et al, Modelling strategies for controlling SARS outbreaks. Proc Roy Soc B 271 (2004): 2223-2232. The BIRS site is excellent and helps facilitates interaction of participants.

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Sam Buss, Professor of Mathematics and Computer Science, University of California-San Diego

I participated in two conferences recently, one in Vancouver, one at Banff. (PIMS vs BIRS, the distinction is unclear to me).

The Vancouver meeting was a very stimulating meeting. It was devoted to E. Nelson's research and for this meeting I wrote what started out as a survey and ended up containing also several new results. As a result of contacts at the meeting, especially with Ed Nelson and William Faris, I was also prompted to write a new formulation of foundational definition of mathematics. This has lead to an article, still in preparation, that would not have been written without the meeting.

The Banff meeting concerned complexity. It had a strong roster of stimulating and exciting talks. For me personally it was invaluable since it exposed me to some of the research that has come up in the past year in complexity theory. In addition, a group of five computer science graduate students from Toronto gave 20 minutes talks each on their work. Their work is very close to my own and it was a great way for me to learn about their work. One of the five is now visiting my own institution (UCSD) for the year.

Both conference venues were outstanding. The Vancouver campus is very pleasant and friendly. The Banff site is absolutely stunning.

(Please feel free to use any portions of this you wish, or to extract portions selectively.)

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Steve Krantz, Mathematics Department, Washington University in St. Louis

My experience in the ``Research in Teams" program last Summer was one of the best of my career. We actually wrote a very good paper «while we were in Banff».

I found the facilities to be delightful, the food very good, the staff to be the height of cooperation and good cheer, and of course the surroundings are divine.

I cannot wait to return. I'm invited to an event next Spring and I really look forward to it.

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Joel Horowitz, Northwestern University

I attended a conference at BIRS on regularization methods in statistics. I thought it was a very stimulating conference, met interesting new people, and learned a lot. The papers that were presented gave me several ideas for new research projects. That doesn't happen at most conferences I attend, so I rate the one at BIRS a big success.

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Eknath Ghate, School of Mathematics, TIFR, Mumbai, India

I have been to BIRS once, for the workshop on Mahler Measures in mid 2003, organized by Prof. David Boyd and others.

I'd like to put on record that I found my visit extremely useful. I was able to interact with a wide variety of people, and learn about the latest developments in the area. My connections from this conference have allowed me to stay in touch with people who are active in this field.

I also found the facilities at BIRS of a very high standard - the rooms were comfortable, the food great etc. and even with jet lag I had a very pleasant one week stay.

I wish you all the luck in your future endeavours.

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Scott Aaronson, Postdoc, IAS, Princeton

I've attended the BIRS Quantum Algorithms and Complexity workshop three times, in 2002, 2003, and 2004. I've found it a stimulating experience in many ways; as an example, two of the three meetings led directly to new research papers. At the first meeting, I gave a talk in which I asked whether quantum computers can provide any speedup for searching a physical region of space, where the main constraint is the finitude of the speed of light. I conjectured that the answer is no. Within about two minutes, Andris Ambainis, who was in the audience, had disproved my conjecture. We ended up developing his idea into a paper on quantum algorithms for spatial search [1], which led to further papers by Childs and Goldstone and by Ambainis, Kempe, and Rivosh. At the second meeting, I told Harry Buhrman (another participant) about a problem I was working on: to give evidence that quantum advice is more useful than classical advice, by proving a relativized separation between the complexity classes BQP/poly and BQP/qpoly. Harry asked why we couldn't just prove an *unrelativized* separation. I'd never considered that before, but by midnight or so, I could prove to Harry that it was impossible with current techniques, since any problem solvable in quantum polynomial time with polynomial-size quantum advice, is also solvable in classical exponential time with polynomial-size classical advice. This result became the basis of [2]. (We were up at midnight because there was an aurora borealis.)

[1] S. Aaronson and A. Ambainis. Quantum search of spatial regions, to appear in Theory of Computing. Conference version in Proceedings of IEEE FOCS 2003, pp. 200-209. quant-ph/0303041.

[2] S. Aaronson. Limitations of quantum advice and one-way communication, to appear in Theory of Computing. Conference version in Proceedings of IEEE Conference on Computational Complexity 2004, pp. 320-332. quant-ph/0402095.

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Chi-Kun Lin, Department of Mathematics, National Cheng Kung University

Thanks for the mail. I attended the inverse problem workshop in 2003 and the team study of kinetic theory and multiple-scale analysis. The BIRS afford a wonderful place to gather the outstanding mathematicians to share and communicate the new idea. Besides the new knowledge, it also give a friendly and stimulating environment that mathematicians can focus thinking some important problems. I really appreciate and really hope to go back to BIRS again.

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Remco van der Hofstad, Technische Universiteit Eindhoven

I participated in the BIRS workshop on `Stochastic Partial Differential Equations' in September 27- October 2, 2003. This was a wonderful experience. The topic is slightly off my usual area of research, and i was very nice to receive an excellent overview of the field. Without this workshop, this would have been much harder.

Furthermore, as a result of the above workshop, I started talking to Vlada Limit (Mathematics, UBC), and we are currently working on a project to apply the lace expansion to edge-reinforced random walks where there is a preferred direction on the basis of these discussions. We hope to complete this project somewhere next year, and we are very grateful to BIRS for providing us with the opportunity to start this up.

Needles to say, BIRS is an excellent place for workshops. Since the surroundings are so spectacular and the workshops are very high quality, almost all participants agree to come. This makes sure that the workshops remain to be of excellent quality. Also, personally, I found the mix between the arts and mathematics quite interesting. At dinner, the participants were typically mixed with artists participating in different workshops or sabbatical, and it was very stimulating to talk to them!

I will come to BIRS again in May-June 2005, and already look forward to this opportunity!

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Jacques Liandrat, LATP, EGIM, University Aix Marseille 2

As an happy coincidence I received today your mail and a mail of acceptance of a paper in ACHA. This paper was triggered by a discussion I had with Peter Oswald in BIRS during a very nice workshop in spring 2003. I can also certify that the workshop in Banff was exactly of the right size and pace to be productive in term of research. The only place I know that can be compared to Banff is Oberwolfach but, to tell you the truth, I prefer Banff!

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Marcus Spradlin, Assistant Research Physicist, Kavli Institute for Theoretical Physics

I participated in the String Field Theory Camp (a Focused Research Group) in July 2004 and found it to be a very rewarding experience. I have attended three other similar workshops, one in the US and two in Europe, but my visit to Banff was by far the most productive. In my opinion, the BIRS provides the ideal work environment, free from distractions and with all necessities conveniently at hand. I was particularly impressed, upon first entering my room, to find a Sunray computer terminal instead of a television. During my one-week stay I was able to make significant progress on a paper I had just started working on with Anastasia Volovich, another participant in the Group. Furthermore, overlapping interests led soon after the completion of the workshop to a collaboration with Mark Van Raamsdonk (one of the organizers of the String Field Theory Camp) on another paper.

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Peter Topping, University of Warwick

Here are some comments from my perspective as a young European mathematician. I attend conferences at Oberwolfach once per year on average and this is a great place to meet European colleagues and the occasional north American. Of the many differences between Banff and Oberwolfach, I noticed at the ``perspectives in differential geometry" meeting that there were many more senior north American participants with whom I would normally meet up less regularly than I would like. (Tian, Schoen, Bryant, and many others....) I look forward to coming again.

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Felix N. Bchi, Head Fuel Cell Systems, Laboratory for Electrochemistry, Paul Scherrer Institut

I had the pleasure to take part in the Fuel Cells Dynamics II Workshop at BIRS in 2003. For me this was a rewarding experience, because the relaxing atmosphere, the common meals, and excellent housing at Corbett Hall at BIRS allowed for many important personal contacts away from the stress of the everyday business.

I would strongly support the continued operation of BIRS. Due to my good experiences in 2003, I will come back for a another workshop in 2005.

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Will Turner, University of Bristol

I found the recent BIRS workshop on Finite Dimensional algebras very interesting and useful. It brought to my attention a number of ideas on preprojective algebras, coinvariant algebras, and algebraic groups, of which I had not been aware. I am bringing some of these notions into my own work, and writing a paper about it, entitled ``On seven families of algebras".

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Chris Budd, Director of BICS, University of Bath

I am delighted to be able to write in support of BIRS. I spent an excellent week at BIRS last year at a workshop on level set methods. I have been to many conference centres around the world and I think that BIRS is the best by a considerable margin. The facilities were excellent, the staff very helpful, and the excellent food and social activities greatly helped the group work together. As a result I accomplished a great deal in the week and the ideas generated led directly to a PhD project. The location is stunning and I found BIRS easy to get to. I would also like to say that I think that the idea of having a large number of high quality week long meetings is an excellent one. Other research centres have opted for having much longer periods of concentration. These are much harder to go to and are much less focused. The week long model is much better. As director of the Bath Institute for Complex Systems (BICS) I am looking forward to close interactions with BIRS in the future and very much hope that we can organise some joint events together.

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Ivan Todorov, Department of Pure Mathematics, Queen's University Belfast

I participated in one of the 5 days workshops at Banff in December 2003. It was an extremely useful conference for my research and carrier since it brought together the world leading experts in the area (Operator Algebras). Being at the initial stage of my carrier, it was very important to me to be able to speak about my results to such an audience. Discussions with a number of participants lead to widening my research horizon and bringing up a number of new problems to work on. I should mention the relaxed atmosphere, the efficiency of the staff and the particularly nice geographical setting of the research station. I hope that adequate financial support for Banff will be found so that it can continue his mission for the benefit of the scientific community.

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Nick Higham, School of Mathematics, University of Manchester

During my Nov 03 workshop http://www.pims.math
.ca/birs/workshops/2003/03w5008/ I found out that a US colleague (who I already knew) was on sabbatical and was interested in visiting me. We discussed research plans and subsequently wrote a proposal for an EPSRC Visiting Fellowship for him to visit the Univ M/cr in 2004. That was funded and I was able to augment the support with locally obtained funding.

None of this would have happened had we not been (a) physically at the same location (b) in a relaxed workshop environment with time to discuss plans and ideas.

Furthermore, the workshop proved an excellent time to advance ongoing joint work with two other US colleagues - again a normal conference would not have been nearly so good.

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Fernando Quevedo, Department of Applied Mathematics & Theoretical Physics, University of Cambridge

I participated at a string cosmology workshop in BIRS in early summer. It was a wonderful experience. Besides the excellent set up ( beautiful landscape, computer in the room, good quality and easy access food, etc.), our workshop ran very well. The place allowed for a very informal workshop with plenty of time for discussions.

There we had a very good experience, starting a successful collaboration with C.P. Burgess, J. Cline, R. Kallosh and A. Linde that ended up in what we consider a very nice article titled `racetrack inflation' which is a novel way of getting cosmological inflation in string theory.

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Wolfgang Dahmen, Institut fr Geometrie und Praktische Mathematik, RWTH Aachen

I have attended a BIRS workshop on computational Harmonic Analysis and Nonlinear Approximation in 2003. I have enjoyed very much the stimulating atmosphere and the nice infrastructure which I found very supportive of informal collaborations. For me it was a good opportunity to continue ongoing work with at least two other participants on adaptive an nonlinear solution methods for variational problems.

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Enrico Rettore, University of Padova

I have participated in a workshop at BIRS on the use of the Regression Discontinuity Design in Economics, May 15-17 2003. Great place, great workshop! A small group of applied economists and econometricians - indeed, a large fraction of those drawing the line in this research field - participated in the workshop making it extremely stimulating. We had several comments on the paper we presented both during and after the workshop which have been of major relevance to improve it. Eventually, we had the paper accepted for publication in the Journal of Econometrics. I also want to add a word to stress how much I found the accommodation comfortable and the surroundings peaceful. Definitely, a trip (from Italy!) worth its cost.

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Sylvain Sardy, EPFL, Swiss Federal Institute of Technology

I greatly enjoyed a workshop held on September 6-11, 2003 at BIRS that gathered a panel of researchers that would have been difficult to put in the same place at the same time without that conference. The two organizers, Dr. Ivan Mizera and Dr. Roger Koenker, did a great job selecting these people with whom it became easy to talk, discuss research projects, and exchange ideas. Among the most fruitful outcome of the BIRS conference, I would like to mention a paper on total variation I submitted a month ago in an American statistical journal. I was also personally impressed by the Canadian hospitality.

I therefore strongly hope conferences at the BIRS will continue to operate as well as they have done in the past for a great future of international scientific collaborations.

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Brigitte Verdonk, Universiteit Antwerpen

The workshop at BIRS has given me the opportunity to meet and interact with many top specialists in the field of model reduction, it has given me the opportunity to obtain a more global view on and at the same time more thorough understanding of the most recent algorithms. This better understanding is essential in some of the current and future projects that I take part in.

Wishing you a successful continuation of BIRS!

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Preda Mihailescu, University of Paderborn

I have spent a 5 days period of time for a workshop in Banff, having the occasion to meet in one (lovely and well entertained) spot, specialists from my larger area of interest, from all over the world, some of which I did know, others yet not. The conditions of the Banff center are in addition marvellous, allowing one to concentrate on work and scientific contacts, while having at the length of hand opportunities to relax - as a natural compensation for the fruitful work done.

I met new very interesting specialists in Banff and this pushed my work ahead - I am certain it will materialize in some new papers which might have taken much longer to mature otherwise. I thank Banff!

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Geert Verstraeten, Ghent University

Last year, I attended the BANFF Credit Risk Conference 2003, and found it an extremely useful learning opportunity. I had just completed the 2nd year as a doctoral student in Marketing, and had recently performed a study on Credit Scoring. Hence, I was a freshman in the domain, and considering my recent study, I was eager to receive remarks on this study from the domain experts, who were almost unanimously present at the Conference. I had the opportunity to present my study during a full hour, and the most respected authority in the domain of my study - who had published a similar paper using a different methodology - was to present his comments during the next half hour, and this was followed by a general discussion. The remarks I received were extremely useful, and the discussion was so useful to my research, that I was able to revise my paper and submit it to JORS (Journal of the Operational Research Society). After one minor review, the paper was accepted for publication and I seriously doubt that this would have been the outcome without the fruitful remarks and experience I received at the Conference in BANFF. To me, this conference was of great value!

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Christine Lescop, Director of Research at CNRS

My stay at the Banff International Research Station was a very pleasant opportunity of meeting people working in North America I had never met before and to learn about many of their interesting results on the braid groups and the mapping class groups. I also appreciated sharing viewpoints on configuration space integrals in low-dimensional topology. This was also an important opportunity of tighten links with researchers from Japan and North America. This was a very interesting and stimulating workshop.

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Kurusch Ebrahimi-Fard, University of Bonn

I am very glad about the fortune I had to come to BIRS last August. This visit was most fruitful to my career. Beside the fact that I could enjoy this tremendous beautiful surrounding area at Banff, the discussions I had at BIRS together with my collaborator Prof. Guo gave rise to another (pre-) publication we just finished. Furthermore, at BIRS I had the chance to meet many interesting senior researchers. This always makes a significant difference in a young researcher's life.

THANK YOU VERY MUCH FOR THE INVITATION!

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Karl-Hermann Neeb, Fachbereich Mathematik, Technische,Universitt Darmstadt

It's a pleasure to write that I've taken part in a BIRS workshop in early September 2003, and it was a very stimulating experience. The topic of the workshop was ``Locally finite Lie algebras'', and the purpose of the workshop was to gather people from all over the world who are presently involved in this very active branch of the structure and representation theory of infinite dimensional Lie algebras. I have profited from the workshop on several levels:

1) The survey lectures on the state of the art on many problems in the field provided a very good overview of the whole subject.

2) I have met several people working on topics very close to my own research, and stimulated by that I started a project with Ivan Penkov on Cartan subalgebras of infinite-dimensional Lie algebras. The outcome was a paper that is already published in the Can. Math. Bulletin. We are now working on a sequel to this paper.

3) I had the opportunity to meet other leading researchers in the field, and we discussed plans for further workshops and meeting. This resulted in particular in an Oberwolfach conference that I am organizing with V. Kac and A. Pianzola in December 2006. It goes without saying that the BIRS workshop are a very nice and useful complement to the Oberwolfach workshops in Germany.

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Janssen, dr.ir. A.J.E.M., Philips Research Laboratories

I visited the BIRS workshop: Applicable Harmonic Analysis, June 7-12, 2003. The emphasis was pretty much on wavelet based algorithms for representation and compression with a strong group of practitioners of this subfield of Harmonic Analysis. My interest is more in Gabor analysis, and some more attendees in that field would have been better for me. However, I fully recognize the potential for intensive and informal discussions, this being guaranteed by having the participants together all the time. You should expect very positive reactions of the sort you are looking for from the subgroup I just identified.

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Anne Siegel, IRISA

I has the privilege to participate to a workshop at Banff institute in June 2004 (aperiodic order) and I would like to mention that this workshop was a pure pleasure from my point a view. It gave me the opportunity to have contact with north-American researchers that I had never meet before. It also gave me the opportunity to understand the deep connections that exist between my own research interest (representation of substitutive dynamical systems) and quasi-cristals. I hope that this will lead to papers next year.

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Matthias Kreck, University of Heidelberg

During the time when I was the director of the Oberwolfach institute, I already wrote a supporting letter for BIRS. It was a great pleasure for me to participate in a workshop at BIRS and to see that the hopes expressed in my letter were all realized. I found the meeting very stimulating. Of course, being an older mathematician, I knew the majority of participants, but I also met some young mathematicians, some of which impressed me a lot. I found the lectures very stimulating. As a result of this workshop, various new ideas came up some of which entered into my present research.

I hope very much that BIRS will continue its extremely useful activities.

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Daan Krammer, University of Warwick

I attended the BIRS workshop Braid Groups and Applications, October 16-21, 2004.

I came with no plans to give a talk, but I did give a talk after people expressed their interest in my recent results. This fact and the audience's response to my talk have greatly encouraged me to write a paper about the topic of my Banff talk.

Most of all I have made connections with some colleagues which may help me get a job which I will prefer over my present one.

For these reasons, the workshop has been one of the most fruitful ones for me so far.

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Eugene Ferapontov, Department of Mathematical Sciences, Loughborough University

I have visited BIRS in the summer of 2003, attending the workshop on Differential invariants and invariant differential equations. This gave me an excellent opportunity to report my recent results on geometry of multi-dimensional dispersionless PDEs and to talk to such experts in the area as Prof. Bryant, Olver, Kamran and many others. Some of the contacts established during this visit have been extremely helpful over the past two years.

BIRS is a stimulating place for exchange of ideas and research in pure and applied mathematics, staying in one row with such internationally recognized centers as Oberwolfach in Germany, CIRM in France, Isaak Newton Institute in the UK, etc.

I feel that it is extremely important to support the activities of BIRS at all levels, and wish all success to its future programmes.

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Aldo Conca, University of Genova, Italy

I attended one meeting at the BIRS in 2003, the meeting on Commutative Algebra and Geometry 03/29 to 04/03.

It was a very stimulating experience. It gave me the opportunity to discuss mathematics with some of the world leaders of the field as well as meeting some of the young talents. At the meeting I met S.Hosten (San Francisco State University). After a long discussion on the possible initial ideals of some kind of toric ideals we started a project , which involves also other colleagues, which is still in progress. I really enjoyed the atmosphere, the organization and the location of the research station.

Thanks again for the invitation.

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Franziska Heinloth (formerly Bittner), Universitat Duisburg-Essen

I participated in the BIRS workshop ``Integration on Arc Spaces, Elliptic Genus and Chiral de Rham Complex". It was extremely useful for me to get together with most of the ``motivic integration people", to get to know what they are working on and what are the new results. Especially I learned about a result which is very close to what I had been working on at that moment, that saved me a lot of time. As I am a beginning mathematician, the workshop was of course also a good opportunity to present my own work. In addition, the BIRS is really a stimulating place, at a very beautiful location.

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Wilhelm Winter, Universitt Munster

I participated at the workshop on 'Amenable Systems', October 30th - November 4th 2004.

The workshop provided an excellent opportunity not only to meet with my collaborator A. Toms, but also to discuss and present some of our joint work on strongly self-absorbing C*-algebras to other mathematicians. The said project is still in progress and it benefited immediately from numerous very helpful comments of and discussions with other participants.

Also, I had very stimulating discussions with N. Brown and P. Ng on a certain problem related to the classification of amenable C*-algebras. Initiated by the discussions during the workshop, I could give a partial solution only two weeks later, and there is a good chance that it can be solved completely in the near future.

Overall, the workshop was an excellent scientific experience, which contributed to the development of the whole area as well as to my personal research projects.

A more detailed account of my joint work work with Toms and of the mentioned problem (with precise statements) can be found in the report I submitted to the organizers of the workshop; I attach a copy as a .pdf file.

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Ronald de Wolf, CWI Amsterdam

I have attended 2 BIRS meetings on quantum computation, one in 2002 and one in 2003. These workshops were probably the most interesting scientific meetings I attended those years, due both to the excellent BIRS environment and the excellent selection of invited researchers. I can think of one, maybe two, papers of mine that originated in these workshops.

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Balazs Szendroi, Department of Mathematics, Utrecht University, The Netherlands

I participated at the workshop Calabi-Yau Varieties and Mirror Symmetry in Dec 2003. In general, I found the atmosphere of Banff Research Station extremely conducive to creative work: beautiful surroundings, ideal conditions, and lots of time to discuss and think. The conference was useful in picking up on the latest work in the subject, especially by Canadian and American colleagues who I meet less often. I gave a talk on ``Calabi-Yau varieties in weighted homogeneous spaces", which was followed by a lively and beneficial discussion; I was pointed to some relevant references, and there ensued a long conversation with another participant, Prof. Todorov, on a possible direction to extend my results. Although this has not yet lead to any breakthrough since, the outcome of this discussion is one of the directions I pursued in my research over the next summer.

I wholeheartedly support extension of the financial arrangements ensuring the existence of BIRS as an ideal mathematics conference facility.

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Dorit Aharonov, Hebrew University of Jerusalem

I would like to testify that the program at Banff I participated in was very fruitful for my research, and very inspiring. The lectures and the discussions have stimulated new ideas - though none of these has developed into a new result yet, I certainly intend to work on some of these ideas in the future. I found it one of the more fruitful and inspiring environments for research I have experienced.

I truly hope to participate in one of the Banff conferences in the near future.

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Bjorn Ian Dundas, Department of Mathematics, University of Bergen

I participated in a workshop at BIRS this spring (03-20 03-25 04w5533 Topology of Manifolds and Homotopy Theory).

The workshop was very inspiring. The timeliness of the conference was clearly felt. Many of the main actors of e.g. surgery theory participated and there was a lively interplay between senior and younger mathematicians. The facilities at BIRS were excellent and the arrangement a success in every way. In addition to the more formal lectures, the mathematics flowed freely also during the short trips in the gorgeous scenery during the lunch break. Important new contacts with recent PhDs were made. I particularly want to commend the organizers for their relaxed and successful problems session in the evening.

On the practical side, having a Sun-Ray in every room made it easy to pursue active research while at BIRS, and preprint servers and MathSciNet were opened frequently during the evenings inspired by talks given earlier in the day.

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Genkai Zhang, Chalmers University of Technology and Gothenburg University, Sweden

This is to testify that I have attended a workshop at BIRS in 2004 and that I have benefited very much from the workshop. BIRS has provided a very stimulating environment and has brought together some world leading experts in the the related areas. During the workshop I have been able to discuss my research problems with quite a number of experts and to understand the related areas, and it has led to consider some further interesting research problems. I hope that BIRS will continue its scientific activities and I express my full support.

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Christian Berg, Department of Mathematics, Universitetsparken 5, Denmark

I found my stay most stimulating and I include below a report I sent to the organizers shortly after the meeting in April 2004:

--- Report on the meeting in Banff, March 27-April 1, 2004

My talk on 'Orthogonal Polynomials associated to positive definite matrices' focused on several new characterizations of indeterminate moment problems in terms of Hankel matrices. This raised the question of how this was related to Riemann-Hilbert problems and brought me in contact with Ken McLaughlin. He had treated asymptotic questions for weights of the form $w(x)=exp(-\vert x\vert^a)$, which for $0<a<1$ corresponds to indeterminate moment problems. He did not know about the problems of determining the order of the entire functions in the Nevanlinna matrices for these problems, and one can hope that this can be done by Riemann-Hilbert methods.

In the talk by Natig Atakishiev was presented some duality results for certain systems of q-orthogonal polynomials. To several people in the audience it was felt that one needed a precise notion of duality in this area, and after several hours of discussions and thoughts I think that he and I have reached such a notion and this could lead to a joint paper.

Jeff Geronimo, whom I did not meet since the Columbus meeting 1989, was now interested in orthogonal polynomials in two variables, a subject I had touched upon years back, so it gave fruitful exchange of information.

I had opportunity to discuss my ongoing project with Ismail on Kibble-Slepian kind of formulas-we came further ahead.

Added December 3, 2004:

I visited Jeff Geronomo and gave a talk at Georgia Tech in November 2004 and visited afterwards Mourad Ismail at University of Central Florida to continue collaboration.

---- I wish great success for BIRS-all the best

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Stephen Wilson, professor of Applied Mathematics, University Of Strathclyde, UK

I attended the BIRS workshop on Nonlinear Dynamics of Thin Films and Fluid Interfaces in Nov/Dec 2003.

I thought that the format and location of the meeting were excellent and that the entire experience of spending a lengthly period of time in close contact with a large number of world experts in their area (in this case thin-film flow) in a relaxed and informal setting extremely academically stimulating.

In particular, the wide range of experts from several scientific disciplines who attended the workshop have significantly widened my own view of the subject. I returned scientifically (and physically!) reinvigorated from the meeting.

I can give the BIRS project my unqualified support and fervently hope that it continues to thrive!

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Hubert Flenner, Ruhr-Universitaet Bochum, Germany

It is a pleasure for me to write about my experience in Banff. I found in Banff a wonderful scientific atmosphere, where I met during the workshop on ``Commutative Algebra" (Sept. 2004) the very top experts of my field of interest. Of particular importance for me was that also people coming from representation theory of algebras were present, and a lot of very fruitful discussions came out of this. For me this was without doubt the most important conference I attended in that year.

The Banff math. institute, although only a couple of years old, is now already considered to be one of the very top institutes of its kind in the world, together with Oberwolfach in Germany and Luminy in France. I am very impressed that during such a short period it could be so professionally organized and received such an excellent reputation among all colleagues.

Last not least I want to mention the excellent staff and the wonderful surrounding, which is very impressive as are the scientific standards.

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Anton Knigavko, McMaster University

I would like to thank BIRS for a nice experience and express my support to this excellent facility.

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Leiba Rodman, College of William & Mary

I participated in the Workshop on Theory and Numerics of Matrix Eigenvalue Problems, at the Banff International Research Station that took place in November 2003. During the workshop, I had many useful discussions with the participants. In particular, I discussed plans for two research expository papers and an advanced level book. The expository papers are now submitted for publication. The book is now in the final stages of preparation.

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Mike Kirby, University of Utah

I participated in the Mathematics and Visualization Workshop held during May. As a young researcher, I was very excited to be invited to participate in such a workshop. One question which always arises when attending such events is whether the time spent in such a small group setting (not a ``high interaction" event like a national conference) is worth it. My answer with respect to my BIRS experience - it was worth it! During my time at the workshop, I was able to discuss many research opportunities in a depth that I would not be able to do at a conference. From discussions in May with fellow BIRS participants, I have submitted one research funding proposal, have another in progress, and have started research collaboration with someone whom I met at the workshop. My time was certainly well spent. I hope that BIRS is able to continue to provide an environment in which scientific interactions can take place.

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John Wakeley, Thomas D. Cabot Associate Professor, Dept. of Organismic and Evolutionary Biology, Harvard University

I was a participant in the workshop on Stochastic Processes in Evolutionary and Disease Genetics organized by Ellen Baake and Warren Ewens. The meeting was a truly excellent one for me. It gave me the chance to have some extended discussions with people whom I had only met briefly before, in particular Martin Moehle, Anton Wakolbinger, Mattias Birkner, Rick Durrett and Ted Cox. This was very important for my research, which has only recently become rather mathematical. I am working on two new projects as a result of these interactions. In addition, I have been invited to a similar meeting at Oberwolfach (on Mathematical Population Genetics) in 2005 where the discussions begun at BIRS can continue. I also have plans to visit Rick Durrett next week at Cornell to talk about overlapping areas of research. Obviously this meeting was a huge success as far as I am concerned, and I would hope BIRS could hold similar meetings in the future. The unique nature (literally) of BIRS allow some great informal, but highly intellectual, interaction (e.g. on various hikes).

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Jacob Rasmussen, Princeton University

I attended your workshop on ``Floer homology for three-manifolds" last November. My experience there was absolutely spectacular. I can honestly say that it was the most stimulating and productive conference I've ever attended. The research environment - especially the common area and mealtimes - was very well set up to stimulate discussion and the exchange of ideas. I met a lot of new people, and got to spend more time with people I already knew than I otherwise would. The conference was also very productive. Probably everyone who attended will tell you about Eliashberg's theorem that weakly fillable contact manifolds are fillable. This is an enormous result, leading to Kronheimer and Mrowka's proof of property P (among other things.) On a smaller, more personal level, discussions at BIRS led to some of the work in my preprint on ``Khovanov homology and the slice genus." Needless to say, I would leap at the opportunity to attend another conference at BIRS.

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Emanuel Milman, PhD student, Weizmann Institute, Israel

My name is Emanuel Milman, and I am a Mathematics PhD student at the Weizmann Institute in Israel. I attended the July 2004 workshop on convexity in high dimensions at BIRS. I wish to express my gratitude to the organizers and to financial institutions that support BIRS for making the workshop possible and for inviting me there. The hospitality and the conditions for performing scientific research were excellent, and I hope that other students and researchers from all over the world will have an opportunity to benefit from these optimal conditions in the future as well. I have met many people in my field of research, and both personal and professional relationships have been formed (Prof. Alex Koldobsky is one that I mention in particular). My week in BIRS was very productive and inspiring, and I know that I am not the only one.

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Siu O'Young, Associate Professor, Memorial University of Newfoundland

We attended a PIMS workshop last May, and were able to make connections with the aerospace research organization in Alberta for the advance of our research into Autonomous Aerial Vehicles.

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Brigitte Servatius, Worcester Polytechnic Institute

I was a participant in the workshop on Modeling Protein Flexibility and Motions. I am a mathematician and it was a completely new experience for me to work with biologists. The result was rewarding. The discussions started in the presentation rooms were continued during meals and on beautiful mountain hikes even on the way to the airport. The work started at the workshop on molecular allostery will soon show some results. The two mathematical questions I posed before the workshop started, were answered during the workshop (partly worked out on a hike) and will soon be submitted as: The $2$-Dimensional Rigidity of Certain Families of Graphs the authors being Bill Jackson, School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, England. Brigitte Servatius and Herman Servatius

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Nick Patterson, Broad Institute, Massachusetts Institute of Technology

I attended a workshop on Mathematical Genetics at BIRS in Summer 2004. The facilities and organization were superb. I think as a result I was able to generate a number of promising new ideas, and with the help of a colleague at BIRS completely solve a problem that had been ``on my plate" for at least a year.

The contrast with another conference I had attended that summer (in England) was especially striking; the difference was night and day and all in favor of Canada!

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Hugh Couchman, Hugh Couchman, Professor, Physics & Astronomy Scientific Director, SHARCNET, Department of Physics & Astronomy, McMaster University

I have attended one workshop at BIRS November 2003. I thought that the setting was excellent, with all appropriate facilities provided. It was particularly valuable to have easy online access in the rooms including laptop hookup. The venue provided for excellent scientific interaction.

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Pavel Pudlak, Academy of Sciences of the Czech Republic

The workshop that I attended this summer was very important for my research. I learned about new very important results about the subject I was working on (constructive Ramsey theory) when they were still very fresh. The format of the BIRS workshops is ideal for communicating results that are not ready for ``big" conferences or for journals. The beautiful nature in Banff is not distracting, but rather stimulating. Often discussing mathematics during a walk is better than at a blackboard. Several participants stayed in Banff after conference as I did, thus I had more opportunities to exchange ideas with them.

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Sara Biagini, University of Perugia and Scuola Normale

I have participated in June to the Workshop 'Semimartingale theory and practice in Finance'. My impression is that the organization was perfect, both scientifically and practically speaking. Since the invited people were a (relevant) part of the outstanding specialists, it was very stimulating for my research. And this also because we were really living together and there was so much time to discuss (during breaks, meals, after dinner). A paper of mine, joint with Prof M. Frittelli, has greatly benefited from the suggestions derived from that occasion. The facilities of the Center are also remarkable. I particularly appreciated the possibility of working in the room (there was a large desk and a computer, with web connection).

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Peter Ashwin, University of Exeter

I participated in the workshop

Symmetry and Bifurcation in Biology

at BIRS 31/5/03 to 5/6/03 and would like to state that this was one of the most productive meetings I have ever attended. The scientific programme, atmosphere, facilities and setting were second to none, and I managed to set up many new contacts as well as building on previous collaborations with participants. Partly as a result of this I have steered my research into a new and I believe promising direction. I will certainly return to BIRS at the next opportunity I have!

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Lloyd Kilford, California Institute of Technology

My joint paper with Kevin Buzzard, ``The 2-adic eigencurve at the boundary of weight space", was mainly written at the BIRS workshop ``p-adic variation of motives" in December 2003. This provided some free time for Buzzard to write down many things which had not been written down prior to the workshop.

I also found it useful to meet other people working in similar fields to mine (particularly Payman Kassei, Graham Herrick and Fernando Gouvea).

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Peyman Gohari, Concordia University

In May 2004 I attended a 2-day Workshop hosted by The Banff International Research Station (BIRS) entitled ``Decentralized Discrete Event Systems: Structure, Communication and Control". More than 25 researchers who were working on similar problems gathered together to discuss their latest findings.

In terms of benefits and relevance to my research the BIRS workshop stands above any other conference or workshop that I ever attended in my entire academic life. For the first time, I attended-with great interest-every talk. The workshop also provided an ideal opportunity to forge new professional relationships and strengthen the existing ones. Shortly after the workshop, I, together with two colleagues, Dr. Peter Caines from McGill University and Dr. Sophie Pinchinat from IRISA, Universit de Rennes, whom I met for the first time at BIRS, applied for funding for a joint research project. Shortly after that I nominated (and she was subsequently appointed) another colleague Dr. Laurie Ricker whom again I met at BIRS for the first time to be appointed as an adjunct professor at Concordia University so that we can conduct, and apply for funding, for joint research projects and co-supervise graduate students in future.

All of this thanks to a two day workshop hosted by BIRS last summer.

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Knut Aase, The Norgegian School of Economics and Business Administration, Bergen Norway

I attended a workshop at BIRS during the summer of 2003. This is a superb location for scientific thinking, where one gets a lot of inspiration from the magnificent nature in Banff. I was able to write a paper: ``Jump Dynamics: The Equity Premium and the Risk-Free Rate Puzzles", based on this seminar, which I am rather pleased with. Hopefully it will be published in a good journal.

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Weiqiang Wang, University of Virginia

BIRS at Banff is an ideal meeting place for mathematicians. I have been to many top math institutes all over the worlds, and BIRS is among the most impressive and enjoyable ones. I have attended two totally different workshops at BIRS in the last two years, one geometric and one algebraic. Also, I am eager to go back to attend another one in Spring 2005.

Some significant features of BIRS workshops I am most impressed of:

1.The participants are a good mixture of ACTIVE mathematicians (faculty and postdocs) from North America, Europe and Asia, etc.

2. they are focused on the interactions of different fields and/or subfields.

3. doing and talking mathematics in such a beautiful environment at Banff is most enjoyable.

As a specific example, in the ``Workshop on Interaction of Finite Dimensional Algebras with other areas of Mathematics", September 25-30, 2004, I met a group of active mathematicians in Finite-dimensional Algebras for the first time, and was exposed further to the connections between Lie theory and finite-dimensional algebra. One project I am working on now is very much in this direction.

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Andrea L. Bertozzi, Professor of Mathematics, University of California Los Angeles

Regarding a new contact, I have hired and am now collaborating with a postdoc, Dejan Slepcev, whose work I got to know from our thin films workshop last year. He was at the time a postdoc in Toronto working with Mary Pugh and she introduced me to his work as part of that workshop. I am very happy to have this connection.

I participated in the imaging workshop this year and found it to be an excellent program. I had many interesting scientific discussions during this time period and got a lot out of the meeting.

BIRS is a valuable resource.

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Jonathan Crook, Director, Credit Research Centre, University of Edinburgh

I attended a Workshop lasting about 5 days in September 2003 on credit scoring. It was an extremely beneficial event for me. Although the number of attendees was around 30 I met several researchers in my area whose work I was not previously familiar with. I have kept up with some of these since then. It also enabled me to make contact again with researchers in the area who I had not seen for some time and who are based in several different countries. The meeting was extremely productive in terms of enhancing my own research and there was considerable synergy created in the discussion that took place. One outcome is that I am now coauthoring a paper on reject inference which was conceived at the meeting. Indeed whilst at the meeting we penned a number of potential collaborative research projects.

It would be extremely beneficial to have a similar event in the future.

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Abby Thompson, Department of Mathematics, University of California-Davis

I was a co-organizer of the workshop ``Topology in and around dimension three" in September 1003. It was a fantastic experience (and one that I and my co-organizers are anxious to try to repeat- we're applying to run another workshop in 2006). All the practical arrangements were taken care of for us, with remarkable efficiency. That left us in the position of organizers with very little to do except to participate fully workshop itself. Living and working with the forty participants for the week provided the basis for much collaboration and was the start of many new ideas. I got at least one paper from it myself, and know of several others that had their start during that week. In addition I have a graduate student and a postdoc at UC Davis who attended the workshop, and they were inspired by the lectures and especially by the chance to work closely with the more established researchers at the conference. BIRS is a perfect set-up and setting for promoting excellent research. Best of luck with your renewal.

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Rachel Pries, Department of Mathematics, Colorado State University

At my institution there are not many people I can talk with mathematically and the teaching duties take a lot of time when you are a young faculty member. Spending a week in Banff doing only research with many people close to my area was extremely valuable. It helped me finish my paper ``Deformations of curves with a wildly ramified group action". I also heard a classical music concert there which was beautiful.

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Simon Levin, Princeton University

I have attended one Banff meeting so far, and am involved in organizing a second. The first was an outstanding experience, even better than the several excellent experiences I have had at Oberwolfach. The meeting was first-rate, the facilities awesome, and the staff helpful and outstanding.

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John Dennis, Rice University

I recently attended the PNWNAS meeting at BIRS. This is an annual series that serves to keep regional computational mathematicians in contact. The meetings are uniformly high caliber. A very nice thing is that new young faculty members are generally invited to speak. This year I met Michael Friedman, a new Stanford grad who has just joined the faculty at UBC.

I have been to many meetings at Oberwolfach, and indeed I have co-organized meetings there. It would be an overstatement to say BIRS is directly comparable to that wonderful facility, but, BIRS is certainly the closest thing we have in the new world. Keep it up, and keep improving. BIRS is terrific now, and I am sure that it will be even better.

I have an ongoing collaboration with Professor Charles Audet of Montreal and Boeing and Exxon Mobil. It had occurred to me that BIRS would be a terrific place for our next workshop. Maybe you will hear from me again!

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Martin Barlow, University of British Columbia

I have now attended two meetings at BIRS (SPDE in autumn 2003, Stochastic Analysis in April 2004). Both we excellent meetings in scientific terms.

The foreign participants were very impressed with BIRS and Banff. I recall one participant at the Stochastic Analysis meeting telling me that he came just because Zambotti (who was at the first meeting) had told him how good it was.

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Omayra Ortega, Department of Applied Mathematics, University of Iowa

I had the pleasure of attending a summer school on infectious disease modeling titled ``MITACS-MSRI-PIMS Special Program on Infectious Diseases" at the Banff International Research Center in Banff, Alberta. I believe the dates were 6/19 through 7/2. I was also invited to the conference afterwards, but I needed to come back to Iowa City and take a PDE comprehensive exam.

I learned many new techniques that I have already and will continue to apply to my dissertation research on modeling vaccination strategies for rotavirus. I was able to consult with Fred Brauer, James Watmough, Pauline van den Driesshe, Mark Lewis, and Linda Allen. These are some of the most prominent people in my field as well as authors of papers that I frequently reference. Being able to talk with them about my current research and collaborate with them on mini-projects during the summer school was a great resource to me and an experience that I will remember for the rest of my career.

I am grateful that this research center was established and appreciate the center's commitment to uniting disparate researchers in the mathematical sciences. I hope that I will be able to return to the Banff International Research Center to collaborate with other great minds in the future.

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Daniel Ruberman, Brandeis University

I took part in the workshop ``Topology in and around dimension three" in Banff between 09/13 and 09/18, 2003. I sent the following message to the organizers after the meeting, in response to their request for comments. Feel free to use it in your renewal application.

As one of several people who were there with interests ``around" dimension 3, rather than in hard-core 3-manifold theory proper, I found it to be a valuable conference on several levels. On the whole, the lectures were interesting, and there was a good variety of topics. Perhaps the most important opportunity for me was to talk at some length with some of the younger people in the field, whom I generally do not know well. I also found that some of my conversations with more established people were very useful; for example some discussions with John Etnyre may be helpful in advancing a project of mine relating contact geometry and homology cobordism. (As his interests are in contact geometry rather than in 3-manifold topology per se, this might also be viewed as a positive outcome of the broader mix of people at the conference). Finally, I got a chance to meet and talk with David Krebes (who came up daily from Calgary) about some things related to his thesis (about 4 years ago). In the course of a few breaks and conversations over meals, we seemed to have solved a problem in knot theory that was raised in one of his papers. This was not a 'breakthrough', but should result in a nice paper.

It really was an enjoyable week; thanks for the invitation and for running things so smoothly.

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Michael Balogh, Department of Physics, University of Waterloo

I participated in the Nov 2003 BIRS conference ``Galaxy formation: a Herculean Challenge". The participants were among the very best international experts in the astrophysics of galaxy formation, and I had the opportunity to interact with many people whom I had not met at previous conferences. In particular, presentations by James Wadsley, Matthias Steinmetz and Rob Thacker introduced me to new research results that I had not seen before, and that have strongly influenced the subsequent direction of my own research. I am currently beginning projects with Thacker and Wadsley that were largely motivated by results at this meeting.

The meeting also provided me the opportunity to meet with collaborators with whom I had begun work earlier, in an environment that was very conducive to making progress on our research. Progress on the following papers was made during this meeting (co-authors Babul and McCarthy were at the meeting):

Balogh, M., Babul, A, Voit, G., McCarthy, I., Jones, L., Lewis, G. & Ebeling, H., `` An analytic investigation of the origin of scatter in observed X-ray properties of galaxy groups and clusters.", in preparation.

McCarthy, I., Balogh, M., Babul, A., Poole, G., Horner, D. & Holder, G. 2004, ``Models of the ICM with heating and cooling: explaining the global and structural X-ray properties of clusters", 2004, Astrophysical Journal, 613, 811

The workshop at BIRS was an excellent experience and one of the best scientific meetings I have attended, in my 10 years as an astronomer.

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Sandeep Kulkarni, Michigan State University

Unfortunately, due to unexpected circumstances, I was unable to attend this workshop. However, based on the my discussion about the workshop with others who attended, it was very beneficial. When a similar workshop is arranged in future, I will certainly be interested in attending it.

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Jon Alperin, Department of Mathematics, University of Chicago

It is very good news that PIMS hopes to not only continue its Banff program but to expand it as well. I spent a week there for one meeting and it was a very productive and interesting meeting, the institute was exceptionally well run and, of course, it was near idyllic being in Banff.

These programs are now an important international fixture and may they continue and grow.

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Penny Haxell, University of Waterloo

I organised a FRG at BIRS in May 2003, on Regularity of Hypergraphs. This was a very successful meeting. As requested by BIRS, I sent a report on the activities of the meeting, please feel free to quote from that report anything that would be useful as a testimonial for your renewal proposal. I would add the extra information that two problems that we worked on as group projects in our FRG have turned into papers: one is

The Ramsey number for hypergraph cycles I, P. Haxell, T. Luczak, Y. Peng, V. Rodl, A. Rucinski, M. Simonovits, J. Skokan, recently accepted subject to minor revision to the Journal of Combinatorial Theory, Series A, and

The Ramsey number for hypergraph cycles II, P. Haxell, T. Luczak, Y. Peng, V. Rodl, A. Rucinski, M. Simonovits, J. Skokan, in preparation.

The BIRS facility is first-class and I am sure it will continue to make a great contribution to mathematics.

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Peter Hoyer, Department of Computer Science, University of Calgary

BIRS is the most attractive location worldwide for a research workshop and has been very successful in attracting the best researchers from around the globe. Other excellent research stations are The Fields Institute in Toronto, MSRI in California, Aspen in Colorado, and Dagstuhl in Germany, but BIRS is still my favorite location. The settings are ideal for discussions, interactions, reflections, and explorations. BIRS is a gem that puts western Canada on the international research map.

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Florin Diacu, Department of Mathematics, University of Victoria

I fully agree with Don's assessment of BIRS. Our Celestial Mechanics conference was a tremendous success. But for me BIRS means more. The two other events I attended (those organized by Chandler Davis and Marjorie Senechal) have helped me with my book on chronology. The input and the discussions that took place after my presentation were extremely helpful.

BIRS is indeed an exceptionally good initiative, which should be maintained at any price.

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Fred Brauer, Department of Mathematics, University of British Columbia

I was one of the organizers of a summer school and workshop on modelling of infectious diseases at BIRS in June - July, 2004. We all felt that this was a great success because we were able to assemble a group of people with diverse backgrounds and different levels of experience and put them in sufficiently close contact to achieve real exchanges of knowledge and perspectives. The facilities at BIRS were ideal for this purpose; students spending a lot of time in close contact, both scientific and social, and working together on group projects gained a great deal. The organizers believe that the school was a good start toward the establishment of a cadre of developing scientists interested in using mathematics sensibly in epidemiological problems.

The workshop which followed the school was an opportunity for some of these developing scientists to interact with a group of more experienced workers, as well as for these more experienced workers to exchange ideas about epidemiological modelling. The interdisciplinary contacts will certainly lead to future interdisciplinary cooperation and research.

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Gemai Chen, Department of Mathematics and Statistics, University of Calgary

I was extremely impressed by the efficiency BIRS was organizing meetings and the excellent arrangements made to make the participants feel at home. As a result, I want to organize meetings to be held at BIRS and I have submitted a proposal.

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Saurya Das, Assistant Professor, University of Lethbridge

This letter is in support of renewal of BIRS, Banff. I had attended a two day meeting in August 2003 co-organised by the Institute of Theoretical Physics, University of Alberta and held at BIRS. The meeting had been quite useful to me. I presented an invited talk and discussed with several colleagues during the meeting. I hope there are more such meetings on fields of my interest (Quantum Gravity/Mathematical Physics) in the near future which I can attend. Please do not hesitate to contact me if you need any other information.

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Lawrence Peterson, Department of Mathematics, University of North Dakota

I attended the workshop on ``Conformal Geometry" held at the Banff International Research Station in Banff, Alberta, July 31-August 5, 2004. I feel that my attendance at the workshop was worthwhile. During the workshop I met with William Ugalde, and we discussed a new project. Since then the two of us have worked on the project, and we have submitted a related grant proposal to the US National Science Foundation. During the meeting I also briefly discussed an existing research project with Rod Gover. The conference provided an opportunity for me to establish and maintain contacts with other researchers in my field. I am grateful to the Banff International Research Station and to the organizers who invited me.

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Shigeki Akiyama, Department of Mathematics, Niigata University

I spent 1 week there to meet mathematicians very close to me in subject to discuss with. From then, several new project had begun and it still continues with Y.Wang, V.Sirvent and B.Solomyak. The place, food and faciltis were excellent and I am sure these circumstances helped us much to begin new things in brand new direction. Thank you again!

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Elizabeth Thompson, Department of Statistics, University of Washington

I very much enjoyed the workshop Stochastic processes in evolutionary and disease genetics 04w5015, August 7 to August 12, 2004

It was the most interesting meeting I have been to in quite a while, and brought together a lot of people I don't normally see at a single meeting. It was very useful in bringing together ideas from several areas of research in which I am involved. It was also most useful for my student who attended as a student observer. It would have been nice if there could have been a few more than the 2 student observers.

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Michael Neubert, Associate Scientist, Biology Department, Woods Hole Oceanographic Institution

I write having just returned from the BIRS workshop on the mathematics of ecological invasions, organized by Mark Lewis, Pauline van den Driessche and Mark Kot.

The meeting was fabulous. Just the right balance of lectures and unscheduled time to meet some of the most important people in the field. I have come away with at least two new collaborations, a completed manuscript, and many new ideas.

I look forward to future meetings at BIRS--perhaps some that I will try to organize myself.

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Kirsten Fagnan, University of Washington

I participated in the Pacific Northwest Numerical Analysis Seminar workshop during September of this year. As a second year graduate student I found it to be an invaluable opportunity to learn more about research in numerical analysis and meet people in close proximity to the university of Washington with similar interests. I also met several graduate students from other universities and have remained in contact with them.

The presentations at the conference were well done and many were relevant to the project I am working on for my thesis. The workshop was well-organized and provided a good environment for discussion.

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Danny Dyer, Department of Mathematics, University of Regina

In the past year, I have had the privilege to participate in a workshop at the Banff International Research Station. The workshop was wonderful, not the least because of the wonderful setting and the diversions provided by the town of Banff. Indeed the excellent food at BIRS made ``dining-in" at the residence a pleasure!

More importantly, the workshop I attended allowed me to meet with fellow mathematicians interested in graph searching. From discussions with Richard Nowakowski and Gena Hahn (the latter a person I met for the first time at the workshop) I was able to develop new directions to take my just complete PhD work.

In short, I enjoyed myself immensely at BIRS, found it professionally a very profitable meeting, and hope to get a chance to return there for future workshops.

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Katherine F. Stevenson, Department of Mathematics, California State University

I attended a BIRS meeting in September of 2003. It was organized by David Harbater on Galois Theory. It was quite useful to me as it was the first significant conference that I had attended after the birth of my two children (17 months apart). The format of having an intimate and focused conference with not too many talks, was perfect for me. It allowed me to get caught up with what everyone else was working on, and I had time to follow up on what interested me during the breaks and meals. The conference or workshop also had a direct effect on my research. By attending the conference, I was able to restart a collaboration with David Harbater. This resulted in our completing a 30 page paper this fall that has been submitted for publication in a volume in honor of Michael Artin's 60'th birthday. The title is ``Local Galios Theory in dimension 2."

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Robert Craigen, Department of Mathematics, University of Manitoba

I was at a 3-day PIMS workshop on Combinatorial Matrix Theory at BIRS this Spring. I found the environment there, and the service of the staff, to be exceptional, and the atmosphere more relaxed and productive than most conferences because so many of the logistics were well in hand, leaving participants to concentrate on their academic exchanges. The facility is well-designed for a workshop of this size, and I plan to propose some similar events in the near future; the facility and program is unique in Canada and has created a level of academic exchange that is hard to duplicate in other types of facilities.

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Artyom Shneyerov, Assistant Professor of Economics, University of British Columbia

Participating in the BIRS workshop last spring was very useful for me. I got a lot of feedback on the paper I presented, and also met with researchers that otherwise would be difficult to meet in person and informally chat with. I am currently working on a manuscript ``Dynamic Matching with Two-sided Incomplete Information and Participation Costs: Convergence and Existence" that uses some of the ideas from the workshop. The quality of presentations was very high and I would certainly be interested in participating again.

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Ingrid M. Parker, Department of Biology, University of California-Santa Cruz

I just returned from a workshop at BIRS, and I wanted to express my deep-felt gratitude for having the opportunity to participate in the workshop. I met several people I have always wanted to meet, and had an incredibly stimulating and intellectually satisfying trip. The international scope was particularly unique, in my experience. The setting and format of the meeting were perfectly suited to inspiring new ideas and new collaborations. In fact, I came away with ideas for two new papers.

Thank you so much for hosting this event, and others like it.

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David McKinnon, Department of Mathematics, University of Waterloo

Indeed I did participate in a BIRS workshop this past year - in fact, it was just last month. I can honestly say that it was the best conference I have ever attended.

There are many reasons for this. First of all, the surroundings were very pleasant, but then, most conferences are held in pleasant surroundings, so this was not remarkable. Nevertheless, hiking up a mountain and along a river are exhilarating ways to spend an afternoon.

Most importantly, however, the BIRS workshop allowed me to have a great number of lengthy and productive conversations with colleagues from as far away as Australia. After the workshop, I had at least four times as many exciting ideas to pursue as I did beforehand. In just five days, I started active research collaborations on three different projects, each with a colleague with whom I had never worked before. These range from finding integral points on a certain K3 surface to an investigation of Vojta's Conjecture on the blowup of a Jacobian surface.

The most promising project, in fact, is one which brings together the work of Jordan Ellenberg and Akshay Venkatesh with mine, on uniform estimates for the distribution of rational points on rational curves. We're quite hopeful that the general approach of Ellenberg and Venkatesh will be compatible with the more precise results I obtain for lines.

Of course, the beginning of a research project is a very uncertain time, and many of these projects may not come to fruition. But the mere fact that so many productive conversations were packed into so short a time is a powerful testament to the effectiveness of the BIRS workshop as a vehicle for communication between mathematical researchers. Moreover, I was not alone in my sentiments: the two colleagues of mine who shared my shuttle back to Calgary agreed that the workshop was the best they had ever attended, and at least one other of my colleagues was inspired to send forth a proposal of her own for a BIRS workshop in the future. BIRS is a fantastic asset to the mathematical community, and I wholeheartedly endorse it.

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Hongwei Zhang, Ohio State University

It has been a great experience for me to attend the 2004 BIRS International Workshop on Self-stabilizing Distributed Systems. I am PhD student, and I got the chance to talk to many other experts in the field, and exchange our thinking.

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Klaus Hulek, Department of Mathematics, University of Hannover

I participated in 2 workshops in Banff and found both of them most stimulating and useful. The first of these workshops was ``Commutative Algebra and Geometry" (03w5005). After the end of the workshop I spent some more days at BIRS working on a research in team programme with M. Green, D.Eisenbud and S. Popescu. This gave us the chanced to make substantial progress on a project which we had been working on for more than 2 years. This collaboration finally resulted in the following two papers:

math.AG/0404517 Small schemes and varieties of minimal degree. David Eisenbud, Mark Green, Klaus Hulek, Sorin Popescu.

math.AG/0404516 Restricting linear syzygies: algebra and geometry. David Eisenbud, Mark Green, Klaus Hulek, Sorin Popescu.

The meeting in Banff was crucial for us for completing these two papers.

The second meeting I attended was ``Calabi-Yau varieties and mirror symmetry" (03w5061). I found this meeting also very stimulating and had very fruitful discussions not only with mathematicians but also with some of the physicists who attended this workshop. I am still working on a joint paper with H. Verrill which originated from discussions started at this meeting.

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Michiel van den Berg, Department of Mathematics, University of Bristol

I had the pleasure to participate in the Workshop ``Stochastic Analysis" over the Easter 2004. I was hugely impressed with both the facilities of BIRS , the attentiveness of the staff and the quality of the participants/programme.

To have a centre with say an ``Oberwolfach like programme" at your side of the globe is extremely useful since it is more likely to attract participants who would not necessarily make it all the way to Germany.

I very much benefited from discussions in particular from those with Professors Barlow, Burdzy and Z.Q. Chen concerning a variety of problems (e.g. the hot spots conjecture and problems related to reflecting Brownian motion). I was able to continue my work on a manuscript ``Heat flow, Brownian motion and Newtonian capacity: a refinement of theorems of F. Spitzer and S.C. Port" without interruption. This was also the topic of my lecture at the Workshop.

Of course the surroundings of Banff are breathtaking in all respects, and I hope to have the privilege to visit BIRS in the future.

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Andrew Knyazev, Department of Mathematics, University of Colorado at Denver

I have participated in the Theory and Numerics of Matrix Eigenvalue Problems, BIRS workshop, November 22-27, 2003. It has been a wonderful and stimulating experience that is incomparable to any other workshops I have participated in, except for those organized by the Mathematisches Forschungsinstitut Oberwolfach (MFO), Germany. Both BIRS and MFO allow workshop participants to meet in a closed environment that stimulates communications at the personal level and an easy opportunity for exchange of ideas, which is especially important in mathematics. Still, Banff has several advantages compared to Oberwolfach: it is much easier to travel to Banff for those of us in the North America; it promotes cooperation with Canadian mathematicians, which I think is very important; and last, but not least, Banff itself is a great village beautiful located in the mountains.

The workshop that I attended has been very well organized, with world best experts in the area of eigenvalue problems participating. It has been extremely useful for me personally. The open workshop format and unlimited possibilities for discussions have allowed me to make sure that my ideas concerning the Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) method that I develop have been well understood by all workshop participants.

It has been also a great pleasure to have an opportunity to meet and get to know personally a number of Canadian mathematicians. Stimulating discussions with Carrington (Montreal) have attracted my attention to large eigenvalue problems in quantum dynamics, and I have started doing research in this new area, which has resulted, e.g., in the implementation of the LOBPCG in a public software code Abinit for quantum dynamics.

A new cooperative project with Lehoucq (Sandia, Albuquerque) on the stopping criteria for preconditioned eigenvalue solvers, such as LOBPCG, has also been originated during the workshop. The joint paper is in progress.

To conclude, I highly support BIRS as a unique place where mathematical research and discussions can be conducted under the best conditions, and I hope that that BIRS request to expand the operations to 48 weeks per year instead of 40 is approved. BIRS is granted.

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Jerry Ostriker, Institute of Astronomy, University of Cambridge

The experience was great! Most useful workshop that I have been to in years.

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Victor Kac, Department of Mathematics, Massachusetts Institute of Technology

I support the renewal of the BIRS with my great enthusiasm. In 2003 I organised a 3 weeks working in teams program and it was very successful. Though we didn't achieve our main (probably too ambitious) goals, the 3 weeks spent there has lead to a new direction of my research. I find the organisation and the atmosphere of BIRS (which includes a lot of music) very stimulating. A few months ago Roberto Longo and myself have applied to another program at BIRS, so we are very interested in the renewal of the BIRS.

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Masoud Khalkhali, Associate professor of mathematics, University of Western Ontario

I am very pleased that I am given the opportunity to share my experience as a participant in BIRS activities in 2003. I felt I was was very lucky to see our proposal for a ``BIRS workshop on noncommutative geometry''(organized by Alain Connes, Joachim Cuntz, George Elliott, and myself) approved by BIRS. This meeting by all means was a big success and drew a lot of attention in North America, Europe and across the world. Quite a few of graduate students and young postdoctoral fellows from Canada, South America, Europe and States were among the participants as well as the most senior and eminent figures in the field. On an operational level everybody was surprised and pleased to see how smoothly things moved and how caring and attentive the BIRS staff were. This despite the fact that we were there hardly after a few weeks of opening the BIRS. On the scientific level I am sure all participants will share their experiences. For me the meeting was specially rewarding because right at that moment I was involved on a collaborative project with Piotr Hajac from Warsaw, Yorck Sommerhaeuser from Munich, and my own graduate student Bahram Rangipour (now in Victoria) and during the meeting we managed to come up with some of our best ideas. Extensive, and very stimulating exchange of ideas during the meeting with Alain Connes played a very important role and convinced us that we are on the right track. Without this meeting it would have taken much longer to finish our paper.

During 2003 I also participated in another BIRS activity on ``New approaches to Novikov and Baum-Connes conjectures''. The format and style of this meeting was very different with a small group of participants focusing on a very well defined problem and discussing the latest developments.I certainly learned a lot of things that otherwise could have not learned that easily. I also fostered long term friendships and exchange with several of the participants that I am sure will have a big impact on my career.

All in all, both as an organizer and a participant, I think the creation of the BIRS was a great idea that will have a huge impact on research in Mathematics both in north America and worldwide. From a Canadian perspective, it is also very pleasing to see BIRS as one of the top destinations for mathematicians worldwide. I enthusiastically support the continuation and extension of the activities of BIRS in the future.

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Anna Vainchtein, Assistant Professor, Department of Mathematics, University of Pittsburgh

I have participated in the BIRS workshop ``Defect and their dynamics" in August 2003. I enjoyed this workshop and the overall atmosphere at BIRS very much. I particularly liked the fact that there was plenty of opportunity to interact with other participants, discuss problems and make new contacts since we all lived in the same place, went hiking together and shared meals. At the workshop I attended, I met and had scientific discussions with several people whose work I have long admired but whom I haven't met in person before, including Peter Bates, Nick Alikakos and John Cahn. I think BIRS is a wonderful place for research meetings and discussions, and I am looking forward to participating in or even co-organizing another workshop.

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Claus Bauer, Dolby Laboratories

I participated at the CAAN 2004 workshop in Banff in August 2004. This workshop was one of the most fruitful and pleasant encounters in the scientific community I remember. The place offered an optimal venue to discuss advanced topics with a small, focused group of experts without any distractions. I got introductions to new fields of advanced research and made valuable contacts. I wish that the Banff facility will continue to be an important center of scientific exchange.

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Igor Nikolaev, Department of Mathematics, University of Calgary

I took part in 5 workshops at BIRS since it was open in 2002. The existence of BIRS is ABSOLUTELY important for me. Actually, I moved from Toronto to Calgary three years ago having in mind this new facility established in Banff.

For example, I issued preprints http://xxx.lanl.gov/abs/math.AG/0312449 http://xxx.lanl.gov/abs/ma th.OA/0310400 under impression of very stimulating talks at the ``Noncommutative geometry Workshop" at BIRS in April of 2003.

BIRS is unique place in the world of such quality and calibre. I thank God such place exists. Keep it going and growing!

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Matt Kerr, L.E. Dickson Instructor, University of Chicago

I am happy to give a short testimonial to this effect:

I was a speaker at the Dec. 2003 BIRS Conference on ``Calabi-Yau Varieties and Mirror Symmetry", organized by James Lewis and Noriko Yui. Although this is not my area, I expected (correctly) that my work on regulators could benefit from importing some of its computational techniques. Not only did I find the BIRS facilities excellent (e.g., computer terminals in the well-maintained rooms); I met with two collaborators and made four new contacts, with one of whom I am now engaged in a research project on Picard-Fuchs differential equations for regulator ``periods". This is easily one of the most important conference centers in North America, comparable for instance to the CIRM-Luminy in Marseille.

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Michael Peters, Department of Economics, University of British Columbia

Thank you for the invitation to last year's mathematical economics conference at BIRS. The sessions were interesting. The working conditions at the conference were excellent, both for collaboration and for putting in a little extra work after the sessions ended. The biggest benefit for me was the realization that mathematicians like Robert McCann and computer scientists like Kevin Leyton-Brown are working on problems that are so closely related to what we do in economics in mechanism design. We haven't yet had enough opportunity to discuss these issues in detail, but I will keep you informed about the research that results from this collaboration.

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Matthew Szczesny, University of Pennsylvania

I participated in the workshop ``Motivic integration, elliptic genera, and the chiral de Rham complex" in the Summer of 2003. The workshop was very successful and stimulating. I met a large number of mathematicians that I had not before (e.g. Francois Loeser, Julia Gordon, Anatoly Libgober, etc.) Discussion with Anatoly Libgober resulted in a paper on the elliptic genus and discrete torsion, which will appear shortly. A number of other directions emerged from those discussion that we are currently pursuing.

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Baruch Solel,Department of Mathematics

I participated in the BIRS workshop organized by A. Donsig and M. Lamoureux on December 2003 (Coordinate methods in operator Algebras).

I want to take this opportunity to express my thanks to PIMS/BIRS for organizing and supporting this conference. It was a very stimulating conference. It brought together researchers in a focused area and provided excellent facilities for interactions between them. The whole setup there encourages professional discussions (whether it is in special rooms set up for that or around the dinner table) and is very helpful.

Sometimes one finds a certain conference helpful and stimulating but it is hard to pinpoint the difference it made for one's research. In this case, however, I can state at least two works that originated there. I met there Prof. D. Kribs and we started discussing a joint project. A month ago we finally submitted the resulting paper to a scientific journal (acknowledging our thanks to BIRS and the organizers of the conference). Another work is a work that was stimulated by new results presented at the conference by Prof. K. Davidson. This work is still in progress. So, at least for me, the workshop was very helpful and I hope you will continue supporting such conferences.

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Gurjar Rajendra, TIFR

Our team consisting of four mathematicians, Professors M. Miyanishi and Professor K. Masuda from Japan, Professor P. Russell from McGill University, Canada, and myself from India spent 3 wonderful weeks at BIRS (July 23-August 14, 2004). Miyanishi, Russell and myself have known each other for more than twenty years. Miyanishi and I have been collaborating for over 18 years. All four of us meet in various conferences around the world. We work in exactly the same area of Algebraic Geometry and have been following each other's work quite closely. But this was the first time we got such a nice opportunity to spend three weeks for a joint project. The research project we undertook was dear to all of us. It turned out that all of us had significant questions to ask. Since we have somewhat different expertise, the different angles of looking at things were very useful for our work and it was a learning process for each of us. Even during our evening walks some mathematical points which had troubled us during our daily discussions occupied our thoughts. Happily, we could finish a very big chunk of what we set out to prove, type the manuscript and submit our report before leaving. The other facilities like food. stay, recreation were very nice. There will not be a better setting for doing research in mathematics than BIRS. The staff of BIRS was extremely hospitable and efficient. In short, this Center as been playing a very important role for international collaborations in mathematical research. Although I spent most of time at BIRS doing mathematics and taking walks it is clear that BIRS is also an important center for other cultural activities like plays, operas, concerts, and so on. Many countries would like to emulate this example.

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Eduardo Sontag, Professor of Mathematics, Rutgers, Steering Committee, BioMaPS Institute for Quantitative Biology, Rutgers

I attended a workshop in the summer of 2003, and organized another one in the summer of 2004, both times in mathematical biology. The BIRS provided a perfect environment, in every respect: scientific, personal, and setting, for interdisciplinary meetings. At the meeting that I organized, we had mathematicians, biologists, computer scientists, electrical engineers, and others from varied backgrounds. The fact that everyone is housed nearby, and meals are taken together, encouraged interaction like I have not seen elsewhere. The conference facilities are just perfect.

I am sure that you will get renewed - it would be crazy not to!

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Thierry Coulhon, president de l'université de Cergy-Pontoise

Je continue en broken english car j'imagine que ma reponse a de fortes chances d'etre traitee par des anglophones.

The workshop on geometry and stochastic analysis in Banff was for me a great opportunity to meet people I should have met long ago ( e.g. J-D Deuschel), to hear about interesting results (I remember the ones by Bruce Driver and his student Thai Melcher), to finish a project with Martin Barlow and Takashi Kumagai which was then submitted to CPAM, to discuss the organization of a workshop in Oberwolfach with Theo Sturm and Takashi Kumagai; finally a very interesting question by Theo Sturm and Laurent Saloff-Coste during my talk triggered a work I am now finishing with Pascal Auscher

I don't think you should mention in your report the last night we spent in the cow-boy bar downtown, attending to a show by the beautiful singer Lisa Hewitt, nor the fact that my laptop was broken by a shock with a pair of skis in the shuttle back to Calgary, but these are part of my memories of this week...

Bonne chance pour ce renouvellement bien merite

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Romeel Dave, University of Arizona

I was invited to participate in the BIRS workshop ``Galaxy Formation: A Herculean Challenge" in November, 2003. This meeting, I can say with certainty, was among the best meetings of the more than dozen I have attended in the past few years. There was excellent turnout among both observational and theoretical astronomers, no doubt in part due to the excellent location and facilities provided by BIRS. As a result, the meeting was focused, lively, and full of new results that helped shape some important directions for my future research. For myself, this meeting was among several that spurred me to investigate the growth of stellar mass in massive galaxies, where observations have resulted in some puzzling controversies.

I sincerely hope that BIRS is given full support for continuing to provide excellent facilities for interaction in a beautiful setting. I would certainly make every effort to attend another BIRS meeting should the opportunity present itself.

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Van Vu, Department of Mathematics, University of California at San Diego

I have participated in two recent workshops at BIRS: Graph coloring (sept 2003) by Bruce Reed (Univ. McGill), Paul Seymour (Princeton) and Convex Geometric Analysis (July 2004) organzied by Nicole Tomczak-Jaegermann (University of Alberta,), Vitali Milman (Tel Aviv University) and Elisabeth Werner (Case Western Reserve University).

I have found both workshops extremely stimulating. I have heard several interesting lectures and learn many new results. Some of these results give me new ideas for my own research. For instance, my recent work with Terence Tao on random Bernoulli matrices is partially motivated by talks presented at the second workshop. The atmosphere at the workshops was remarkable and the view from the dining hall could hardly be better.

I wish that BIRS would be able to continue and expand its workshop series for a long time. This is essential for the mathematics community in North America and worldwide.

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Noriko Yui, Department of Mathematics, Queen's University

I am Noriko Yui, Professor of Mathematics at Queen's University in Kingston, Ontario. Last December (6-11, 2003), I took part in a wonderful 5 day workshop at BIRS on ``Calabi-Yau Varieties and Mirror Symmetry''. I was one of the organizers. The workshop brought together many researchers working on mirror symmetry from different perspectives. This included mathematical physicists, geometers of all kinds (algebraic, arithmetic, complex, differential and symplectic geometers) as well as number theorists. BIRS provided an ideal setting for interactions among participants.

My own field of expertise is in Arithmetic/Algebraic Geometry, and I have been working on mirror symmetry from number theoretic point of view. The workshop gave me a rare opportunity to learn physics around mirror symmetry directly from physicists. BIRS provided an ideal setting for informal discussions among participants, and heated discussions lasted till midnight or even continued to small hours.

The Proceedings of the workshop is planned to be published from the International Press/American Mathematical Society, edited by J. Lewis, S.-T. Yau and myself. All articles will be refereed.

For my own research, two papers have originated from the discussions I had during the workshop, one of which will be included in the Proceedings.

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Kevin Milligan, Assistant Professor of Economics, University of British Columbia

I participated in a conference at BIRS called Microeconomics of Spatial and Grouped Data in April 2004. I found the facilities and staff to be excellent. We were able to concentrate on our scholarship when we desired, and also relax when we wanted to. I interacted with a number of excellent microeconomists at the conference; renewing and developing ties that have already paid professional dividends. The paper I jointly presented at the workshop is in review at the Journal of Econometrics, where we have been requested to send a revision. Our paper benefited greatly from the interactions with others at BIRS.

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Stephen Berman, Department of Mathematics, University of Saskatchewan

Here is my ``testimonial'' for BIRS. I hope it is of use to you and that you are successful with your proposal. I think BIRS serves a special role within the community and plays an important part in facilitating mathematical developments. Best Wishes Stephen Berman

In late September 2004 I attended a workshop at BIRS on ``Interactions of Finite Dimensional Algebras with other areas in Mathematics". As the title suggests this workshop did not consist of one homogeneous group of researchers, but rather, people working on many diverse areas which touch on the central theme of the meeting. The fact is that there has recently been a lot of cross fertilization between quantum theory, infinite dimensional Lie theory, representation theory, and finite dimensional algebras and this meeting was planned so as to enhance this interaction. As such it was most successful.

The meeting served to help educate me about recent research in areas which, although not my own , have a strong interaction with it. This is not a small point as it is notoriously difficult to learn about new developments in a vacuum by oneself. Rather one needs to talk to the people who did the research. I made new contacts at the meeting and also found many people, not in my direct area of research, who had an interest in some of my recent work. Most people at the meeting had similar experiences. In short, I think BIRS provides a wonderful opportunity for mathematicians to interact and learn from each other. I see very few other places where this kind of in-depth interaction takes place (certainly not in the rushed AMS special sessions which leave even the experts in a trail of dust) and think BIRS thus plays a special role within North American mathematics.

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Michael Eastwood, Department of Mathematics, University of Adelaide

I am writing to express my thanks to BIRS for hosting two very stimulating workshops, which I attended in 2003 and 2004. Both were very useful but for quite different reasons. In July 2003 I attended the workshop ``Differential invariants and invariant differential equations". I knew almost no-one at this meeting, though I had read articles by several participants. The conversations I had and contacts I made were invaluable. In particular, I was directed by Niky Kamran and Peter Olver to an unpublished PhD thesis of Peter Delong from 1982, which was very much related to what I was spoke on at the workshop. Comments from Ian Anderson were very useful in an article that I was writing with Jan Slovak. There are other ideas and correspondence initiated at the workshop that have yet to be followed through. All in all, one of the most useful meeting I have attended. In August 2004 I was an organiser of a workshop on ``Conformal geometry". This was a totally different experience since I knew personally most of the participants (and completely understood almost all of the talks!). The talks brought me up to date with the latest developments, exactly as one would hope. Informal discussions were very useful, the most fortuitous being with John Bland on the bus trip back to the airport. He sketched an idea, which we have since discussed at a conference in Beijing. As a result of these conversations, he will visit soon me in Adelaide and we shall spend six weeks working together on this. At the workshop, Thomas Branson, Andreas Cap, Rod Gover, and I put the finishing touches to an article ``Prolongations of geometric overdetermined systems". This involved some quite animated discussions (not possible by e-mail). The facilities at BIRS are wonderful. Certainly, the workshops I have attended have been lively and inspiring. I only wish they were a little longer.

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Frederick Cohen, Department of Mathematics, University of Rochester

My visit to BIRS was extremely interesting and pleasant.

There are at least two projects which started, and would not have happened without my visit to BIRS. Some details are listed next.

I learned interesting mathematics cutting across several areas at this conference. I was able to learn directly by speaking with T. Kohno, G. Lehrer, D. Krammer, S. Bigelow, as well as a student of Dale Rolfsen who gave a lecture at the conference.

Gus Lehrer, and I started to look at an overlap with algebraic groups, their representations, and group cohomology. We have started work on a problem arising from ``centers of mass" in hyperplane arrangements.

Toshitake Kohno raised some very interesting questions about the cohomology of the braid groups with certain twisted coefficients, together with their connection to quantum groups. We are starting to work together on this problem.

BIRS is a fine mathematics institution which should foster significant development of mathematics. My visit was certainly very valuable.

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Michael Baake, Professor of Mathematics, University of Bielefeld

With this message, I want to express my gratitude towards BIRS, which in my opinion is a great addition to the mathematics landscape worldwide, and from which I have profited in many ways by now.

I have seen it being planned at various stages, and had always thought that it is overdue to have an institute like Oberwolfach in North America. Amazingly enough, no such thing existed, and PIMS did very well in establishing it.

I have been up there several times by now, both as a participant and once as an organizer, and think that it is extremely successful. In fact, it might have turned already into some of the best known places in Canada by now.

The nice atmosphere and the high standard of the meetings combine into a unique and perfect environment to foster mathematical research, and I hope that it can continue to add to the excellent reputation of Canadian science in general and mathematics in particular.

In fact, I sincerely believe that its funding should be placed on a permanent (or at least very long-term) basis right away, as I cannot think of any better value-for-money relation in research and higher education at the moment.

With best regards, and best wishes for a successful continuation of the BIRS legacy

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Jan Minac,Department of Mathematics, Middlesex College, The University of Western Ontario

It is a pleasure to respond to your e-mail message about your proposal which is concerned with the renewal of BIRS.

I was a co-organizer, with R. Elman, A. S. Merkurjev, and C. Riehm, of a BIRS workshop entitled, ``Quadratic Forms, Algebraic Groups, and Galois Cohomology," and which was held October 4-9, 2003. It was really quite a fantastic workshop and I once again came to appreciate the wonderful, friendly atmosphere at BIRS where there are truly ideal conditions for carrying out exciting research in mathematics.

All of the people with whom I spoke were truly very happy at BIRS and they enjoyed the workshop very much. The workshop was very active and productive. In fact in this workshop V. Voevodsky announced a solution of the Bloch-Kato conjecture - a milestone in current mathematics. There were quite a few other important developments which originated from this workshop. In particular the work of N. Karpenko, A. S. Merkurjev, M. Rost, and A. Vishik on quadratic forms and Chow groups has formed a virtual revolution in the current theory of quadratic forms. And the Banff International Research Station has played a crucial role in the realization of these quite significant developments!

For my collaborators - N. Lemire, A. Schultz, and J. Swallow - as well as for me - a dream came true when we recently succeeded in determining some Galois cohomology as Galois modules in a very explicit manner. This was our key problem which we had discussed in the BIRS workshop mentioned above (October 4-9, 2003). Our discussions carried out at BIRS were important to our later success in solving this problem.

Very recently with my collaborators - A. Adem, D. Karagueuzian, and J. Labute - we achieved a significant breakthrough in the structure of Galois groups. This breakthrough is a direct consequence of our collaboration together while participating in the BIRS event ``Research in Teams" in 2003 (``Field Theory and Cohomology of Groups," April 26 - May 10, 2003).

I want to thank you once again for having provided such outstanding conditions wherein fellow mathematicians may gather together from all over the world, and work together creating many new and stimulating mathematical ideas, leading to still more exciting research work. Certainly BIRS is helping mathematicians succeed in very important ways with their research ideas, goals and innovations.

To conclude, I can state with absolute certainty that BIRS has been very important to my research, as well as to the research of my colleagues. Working at BIRS with colleagues and collaborators has been productive, stimulating, and enjoyable.

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Raymond J. Spiteri, Department of Computer Science, University of Saskatchewan

I am writing in support of the renewal of the Banff International Research Station. I have just participated in my first workshop at BIRS, but I have been aware of it even from the days when it was still in the planning stages many years ago. My enthusiasm for BIRS is no less today than it was then.

Rather than extolling the virtues of BIRS at great length, I will summarize what I feel are the 3 most important reasons why BIRS should be renewed.

1. BIRS is the only instrument of its kind in North America. This gives Canada a place on the stage of international research. More and more people around the world are recognizing Canada as a place where top-notch research is carried out. The absence of the venue that BIRS provides would certainly do damage to our international research reputation, especially with respect to our commitment to supporting fundamental mathematical research.

2. The fact that BIRS is so heavily subscribed to is a testimony in itself that the institute is making a difference. Proposals typically must apply over a year in advance before they can take place. The selection process then ensures that only the best of the best are hosted at BIRS. To have such an instrument disappear now would mean that either these meetings would have to move elsewhere (and in all likelihood out of Canada) or they would simply not take place. This would be a terrible shame for mathematics and the spirit of community among the researchers, particularly Canadian researchers.

3. Finally, BIRS makes a difference to researchers like few other instruments do. The workshop I attended was a MITACS Theme Meeting, at which 4 different MITACS projects met to discuss their respective research projects and attend a workshop on a common theme. Individual projects also took advantage of this time to meet by themselves. The meeting was of critical importance in establishing short- and medium-term research priorities, goals, and specific collaborative efforts within our own project. Moreover, I personally established 2 collaborations with other projects. It would have been much more challenging to make such progress under normal conditions at a meeting, where facilities are less abundant and convenient and venues for discussion (e.g., at meals and coffee breaks) are more limited. BIRS greatest strength to the individual researcher is that it is a unique place where one can go to focus only on research. We are very fortunate as Canadians to have such an instrument in our own backyard.

I hope that testimonials such as these will allow BIRS to secure funding for its continued operation.

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Edmund Copeland, University of Sussex

I participated in the String Cosmology meeting in June and sent the following reply to Jim Cline. I think it may be what you are looking for. There are no papers from me which have resulted directly as a result of the meeting, but I am hoping to return to Banff with a small group of people in the future to collaborate on a project.

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Edwin Perkins, Department of Mathematics, University of British Columbia

I write as an organizer of a workshop on Stochastic Partial Differential Equations in 2003 and as a participant in a 2-week Research in Teams effort in the summer of 2004. Simply put it is a fabulous environment for discovery and interaction.

I will focus on the second activity. Rick Durrett, Leonid Mytnik and myself had been working pairwise on a scaling limit theorem for a spatial stochastic model for competing species in mathematical ecology. It was essential for all three of us to get together to finish the project. We scheduled the two-week activity to overlap with a meeting on population genetics, which also interested all of us and provided additional stimulus and potential interactions. During the two weeks we found a serious error in our earlier work, corrected it, worked out the one-dimensional case completely (admittedly much simpler than its 2- and 3-dimensional counterparts where the fundamental uniqueness question remains unresolved in general) and essentially completed a draft of the paper, ``Competing super-Brownian motions as limits of interacting particle systems``. It has since been submitted to the Elect. J. Probability.

Ted Cox was a participant in the genetics meeting and I had been working with Ted on some different Lotka-Volterra models. We had managed to obtain a scaling limit and apply it to the question of co-existence of types in the regime where the types prefer to be surrounded with the other type. The co-existence question in the other regime seemed to require a high density limit theorem which was different from ours. We had some guesses as to what the limiting reaction diffusion equations was and one afternoon brought this up with Rick Durrett. We did not think Durrett's earlier work would apply here but after several hours discussion on a couple of separate days it became clear that it did, and we (well Rick) found the limiting equations which were not what we had expected. Still they would predict what we were interested in showing: a discontinuity in the derivative of the critical survival curve at the point where this phase transition between type preferences takes place. There is a lot that remains to be checked of course but we now have a clear program to follow as the result requires both Durrett's earlier techniques and the coalescing random walk calculations Ted and I had been doing.

The point of course is that BIRS provided an engaging environment where we could complete one project and find a very promising path for another.

The facilities at BIRS are fabulous. The computing facilities are easy to utilize and the staff extremely helpful. Organizing meetings is painless and the location means you may expect a very high percentage of your invites to be accepted (we had 30/32 accept). Meeting with other scientists at BIRS allows one to completely engage in science in a way that is just not possible at your home university where there are always administrative and family duties to attend to. PIMS, MSRI, NSF, NSERC, the Banff Centre and the Alberta government should be very proud of their joint creation.

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Eric Shea-Brown, NSF postdoc, Courant Institute

I was a participant in the 2003 Workshop in Symmetry and Bifurcation in Biology, which was without question one of the best meetings I have ever attended. As a direct outgrowth of our discussions at BIRS, I am now collaborating with one of the workshop organizers, Marty Golubitsky, and another of the attendees, Kresimir Josic, on a paper in progress entitled ``Symmetric Networks of Phase Oscillators." This project draws on our different levels of experience and background in algebra, dynamics, and mathematical neuroscience. In addition, I still benefit from the many discussions I had at BIRS over coffee and into the nights, during which many of the fundamentals of equivariant dynamics were explained to me by more senior attendees. I would jump at the chance to immerse myself in the BIRS workshop environment again.

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Krzysztof Oleszkiewicz, Warsaw University

The conference on convex geometry in Banff I participated in last summer was very well organized and very fruitful in scientific sense, as far as I can judge. It was a good (and rare) opportunity to learn what the world-class specialists in this field work on.

Let me praise the unique atmosphere of the Banff center and the wonderful landscapes. The accommodations and food were perfect.

I am sure that BIRS activities serve very well the mathematical community.

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Suresh Nayak, Chennai Mathematical Institute, Chennai, India

I am writing this letter to acknowledge the enormous help I received from the BIRS programme in 2003 for my research.

In August 2003, via the Research-in-Teams programme, I had the opportunity of mathematically interacting in person with Joe Lipman of Purdue University and Pramath Sastry of University of Toronto. The occasion for three of us to meet together in one place came at an important stage in the production of a volume (book) of three research papers by us. The discussions in Banff spread over two weeks enabled us to push a jointly coauthored manuscript towards its final stages and also helped me gain valuable inputs for a separate work of mine. I am happy to inform that both these papers have now reached the publication stage.

I strongly encourage BIRS to continue their present efforts and provide similar opportunities to other research groups.

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Mathematisch Instituut, University of Utrecht, Utrecht, Netherlands

Herewith I would like to express my support for BIRS.

I participated in the BIRS workshop 03w5061 Calabi-Yau Varieties and Mirror Symmetry in December 2003.

I found that BIRS had created a very stimulating atmosphere. The workshop was small scale and all participants were staying in the same building. This made it easy to meet people also at dinner and in the evening and thus get engaged in informal discussions. Such informal discussions in turn are important to make new contacts and to hear about participants' expertise and interests which are maybe not presented in formal talks.

I personally was stimulated through one of those informal discussions to present some results of my research in an after dinner evening talk (1 hour) and to write part of it in a paper for the workshop proceedings.

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Shihoko Ishii, Tokyo Institute of Technology

I stayed in BIRS for one week of June last year. It was really stimulating experience for me to stay there. Actually I learned many new ideas from other participants' talk. We exchanged our ideas and as a result I could developed the discussions into a new paper which will be published in Journal fuer reine und angewandte Mathematik. This is due to the chance you gave me to stay in BIRS. I hope BIRS will have a good financial situation forever.

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Etienne Blanchard, Institut de Mathematiques

I send you a short description of my stay at BIRS last month for a workshop on The structure of amenable systems.

There was quite an intensive programme with many talks (8 per day) But most of the participants could not attending all the talks (apart from the organizers). You had the opportunity to read the different abstracts sent by the speakers, to choose which ones you would attend, to learn from these speakers, to talk with them and then to make progress in your understanding of our mathematical questions.

The very nice atmosphere in Banff (food, classical concerts, visits in the mountains) also gave us the possibility to relax and to `find by accident' new inspiring ideas to solve our mathematical problems.

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Marcelo Aguiar, Department of Mathematics, Texas A & M University

I participated in a 4 day meeting at BIRS in August 2004. It was a very positive experience. I started a number of research projects in collaboration with various authors, some of whom I met for the first time there. The conditions were excellent. I hope to participate in or organize similar workshops in the near future.

I hope the funding agencies make supporting BIRS a priority.

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Elvezio Ronchetti, Chair, Department of Econometrics, University of Geneva, Switzerland

I participated in a workshop at the Banff International Research Station in 2004. It was a very successful focused group workshop on the data analysis of large data sets. As a side effect it helped me to set up a collaborative research effort with some colleagues in the area of financial modeling where large data seta are a key issue. More generally, the Center is located in a beautiful environment which stimulates many discussions and informal contacts and its management is very efficient and friendly. It is indeed a successful example of cooperation which should inspire similar efforts elsewhere in the world.

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Matthias Gaberdiel, Institut fuer Theoretische Physik, ETH Hoenggerberg

I visited BIRS in the autumn of 2003 and the spring of 2004 to take part in the `Research in Pairs' programme `Modular invariants and NIM-reps' with Professor Terry Gannon of the University of Alberta. I found both visits very stimulating and useful. The working conditions at BIRS were excellent, and we were able to concentrate fully on our research. Terry and I had worked together before, but it was extremely useful to be able to spend some uninterrupted time together to work out various vague ideas we had had before and to begin new lines of thought. (While at certain stages of a collaboration it is possible to work at a distance via email, it is sometimes crucial - in particular, at the beginning of new projects - to be able to talk directly; this is what we were able to do in Banff.)

The four weeks we spent at Banff were extremely productive. As a result of both research visits, we were able to make significant progress on problems that had been around for some time. In particular, we could prove that the charges of the twisted branes give rise to the same charge group as for the untwisted branes. We also studied the charges of branes in non-simply connected group manifold, and found intriguing constructions for the D-branes that carry the remaining charges (for SU(n) with n greater than 3). More explicitly, the relevant papers that originated from our research visits to Banff were

M.R.Gaberdiel, T. Gannon: The charges of a twisted brane, J. High Energy Phys. 0401, 018 (2004); hep-th/0311242.

M.R.Gaberdiel, T. Gannon: D-brane charges on non-simply connected groups, J. High Energy Phys. 0404, 030 (2004); hep-th/0403011.

M.R.Gaberdiel, T. Gannon, D. Roggenkamp: The D-branes of SU(n), J. High Energy Phys. 0407, 015 (2004); hep-th/0403271.

M.R.Gaberdiel, T. Gannon, D. Roggenkamp: The coset D-branes of SU(n), J. High Energy Phys. 0410, 047 (2004); hep-th/ 0404112.

I hope this is of help -- please let me know if you need any further information.

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Isaak Rubinstein, Energy and Environmental Physics, J. Blaustein Institute for Desert Research, Ben-Gurion University of the Negev, Israel

This is to testify that I did find the workshop on Computation Fuel Cells Dynamics II at BIRS (May 2003) I participated in highly stimulating. It provided me with a unique opportunity to meet in one place in informal atmosphere a selection of leading experts on fuel cell modeling.

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Peter Swain, McGill University

I attended the `Dynamics, control and computation in biochemical networks' at BIRS during august 2004. The workshop was invaluable in bringing together control theorists, mathematicians, physicists, and biologists. I am an applied mathematician and am excited about the new contacts I made with people in control theory, whom I'm sure will give me a novel insights into my own work.

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Yi Zhang, Center of Mathematical Sciences, Zhejiang University

I strongly support BIRS. I very like BIRS, I have benefited from joining the Workshop ``Calabi-Yau varieties and Mirror Symmetry" held in Dec2003. I got flash ideas in BIRS and knew many good mathematicians. Best regards,

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Tore Schweder, Department of Economics, University of Oslo

I did indeed participate in the BIRS Point Process workshop in the summer of 2003. And it was a most stimulating experience.

I learned about active areas in the theory of stochastic point processes, and particularly about methods of analysing point process data. I also got valuable feedback on my own contribution concerning Hawkes processes and line transect surveys of whales. This has lead to a paper which was submitted to JABES. Without the workshop, I would probably not have been able to get my co-author's attention, and there would have been no paper.

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Andrew Ranicki, School of Mathematics, University of Edinburgh

I attended two meetings in BIRS this year 20-25 March 04w5533 Topology of Manifolds and Homotopy Theory 8-13 May 04w5037 Knots and their manifold stories Both meetings were great successes, giving me an opportunity to meet and talk to many mathematicians in my field. Even in this electronic day and age there is ultimately no substitute for direct contact! In addition, there was the wonderful setting of Banff and the Conference Center, and the friendliness of the staff. I feel very fortunate to have also been invited to a BIRS meeting next year 27 August - 1 September 05w5067 Topology accepting the invitation with great alacrity.

Long may BIRS flourish!

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John E. Cremona,School of Mathematical Sciences, University of Nottingham, UK

Thanks for a fantastic conference which I thoroughly enjoyed. I will send you a longer abstract of my talk shortly. Amongst the many interesting and useful conversations I had I can include: progress on an ongoing collaboration with Michael Stoll and Cathy O'Neil took place at the meeting; and also I had a very stimulating long conversation with Manjul Bhargava on the last evening concerning extensions of his higher composition laws to higher dimensions (which is work he is currently doing with Cathy O'Neil).

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Herbert Abels, Bielefeld University, Germany

I participated in the workshop on new techniques in Lorentz manifolds at BIRS from November 6 to November 11, 2004. I enjoyed it very much. The environment that was created by the research station and its staff was very stimulating. I met a number of people that I had never met before or had not seen for a long time. The talks and the discussions were very good and made me acquainted with work that I had not seen before. Particularly useful were the discussions I had with W. Goldman, T. Drumm and V. Charette on the topic of 3-dimensional space-times and with F. Labourie on his joint work with W. Goldman and G. Margulis on a generalization of the Margulis invariant. Both of these topics are close to my own research work and I am sure the new input will turn out to be fruitful for my own work. With W.Goldman I also discussed and actually showed him the manuscript of a book on proper transformation group that I am writing together with P. Strantzalos. I sent him a copy and hope to continue the discussion about it with him and get further feedback from him.

So in all the conference was very fruitful for me. It gave me new insights, ideas and perspectives, let me renew old contacts and created new ones and started some discourse on research and publications.

Not to forget, my wife and I enjoyed the magnificent landscape. We added a few days in Banff to explore it on hikes.

I am very thankful to BIRS for affording this magnificent opportunity for meeting and having scientific encounters.

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Yuanan Diao, Professor of Mathematics, Department of Mathematics, UNC Charlotte

Last year, I was a participant in the Random Knotting, Workshop in Statistical Mechanics of Polymer Models which was held at Banff International Research Station. This week long workshop brought many researchers from several research areas and provided a very nice opportunity for us to interact. During this time, I was able to finish an on-going research project with several of my collaborators (they were all invited to the workshop by the careful selection of the organizers). I was also grateful that during the discussions with my other colleagues, I have found a few interesting topics to explore further. Although I was asked by the organizer to give a introductory style talk about random knotting, the audience actually asked many interesting questions during my talk, which to me is a real eye-opening experience. I am happy to report that I have published seven papers since I visited Banff last May, three of them were related to the activities initiated at BIRS (the references are given at the end of the email in case you need them). I give my full support for your effort to renew and expand the operations at BIRS and certainly would like to be a participant again in the future.

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Mohammad H.S. Amin, D-Wave Systems Inc.

I attended a BIRS meeting at Banff in Apr. 2003. The meeting in general was very interesting and helpful. I had a chance to meet a number of prominent scientists including Tony Leggett, who won the Nobel prize in physics that year. I was able to talk to Leggett for a few hours describing my work on nonequilibrium superconductivity, which seemingly was impressing to him. I got a number of excellent remarks from him which improved my paper and helped me on a new work which later was published in the Physical Review Letters (the most prestigious physics journal). In general, I think my participation in the BIRS meeting was very helpful and had important impact on my research carrier.

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Tomas Gedeon, Associate Professor of Mathematics, Department of Mathematical Sciences, Montana State University

I would like to add my voice to strongly support continuing funding for BIRS. I have participated in three workshops in the last two years. The organization and the support of the staff was flawless. I also strongly believe that the workshops of small size, with no multiple sections like those supported by BIRS are much more conductive to original research and collaboration then big monster conferences. I also enjoy the fact that all participants are treated equally financially, there are no plenary speakers and there is no conference fee.

This was a brilliant idea and continues to be a brilliant idea. I hope to be coming back to Banff for years to come.

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Shiri Artstein, Princeton University

I have participated in a conference on the geometry of high dimensions last summer at Banff, as a PhD student in the final stages of the dissertation. I am now a Veblen postdoc at Princeton University and the Institute for Advanced Study. The conference gave me a chance to present a large portion of my work to experts in mathematics who share my interests. It was very beneficial, and the comments of people in the community, the top scientists in the field, which attended the conference, were helpful and influential. The facilities and the arrangements were wonderful, and I look forward to attending another Banff conference.

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Christophe Croux, Department of Applied Economics, Katholieke Universiteit Leuven, Belgium

I participated to the focussed workgroup ``Robust Analysis of Large Data Sets", from June 5 - June 19, 2004 in Banff. It was really a fabulous research experience. Plenty of time to talk with other researchers in an informal atmosphere, time for in-depth discussion, ... The International Research Station is perfectly equipped and extremely well organized.

As a result of the workshop, I started a research project together with Ruben Zamar, on robust correlation measures. Another one that started off in Banff was together with Peter Filzmoser, on Robust continuum regression that will appear soon in a journal.

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Jim Cline, Department of Physics, McGill University

I was an organizer for the workshop ``New Horizons in String Cosmology," which BIRS hosted during June 12 - 17, 2004. For me and for many participants who enthusiastically praised this venue, the workshop was a highly stimulating opportunity for exchange of ideas and fostering new collaborations. During this workshop Cliff Burgess, Fernando Quevedo and I joined forces with Andre Linde and Renata Kallosh to produce a paper we called ``Racetrack Inflation," which arguably is one of the first successful attempts to create an inflationary model using moduli of the extra dimensional Calabi-Yau manifold of string theory, within a rigorous and theoretically controlled framework. This collaboration would not have happened without the workshop at BIRS.

I received very positive feedback from participants. Here are some examples.

Andy Albrecht, UC Davis:

``In terms of specific science issues, I feel this meeting was a real turning point. For the first time I felt that a large number of string theory people were ready to focus on very cosmological questions. One important impact of this meeting is that I feel much more connected to the string community, and inclined to engage members of this community in the future."

Geraldine Servant, CEA Saclay:

``The facilities at Banff were amazing. It is a wonderful site for organizing workshops. The number of participants was perfect. This size of workshops is really adequate. It was a good thing that you incorporated some young physicists, including graduate students. It is very stimulating for young scientists to be surrounded by top quality physicists in an informal setting. The workshop also benefited from the diverse group of participants."

Ed Copeland, Sussex:

``I found the meeting not only enjoyable but also very stimulating. The relaxed atmosphere throughout the meeting meant that people were more than happy to discuss the aspects of string cosmology that they found most challenging and uncertain. This was so refreshing. All too often we attend meetings where we feel the need to make it sound like the subject has been sorted out thanks to our latest masterpiece. This was not like that. I don't mean to imply the work presented was not of a high standard. I found that stimulating. In particular the attempts presented by Fernando, Andre, Renata and Eva to obtain inflation in string theory, and the search for observational signatures of strings are exciting developments."

Alan Adams, Harvard University:

``...Much more important than any concrete progress reports, however, were the many intense and entertaining personal interactions between cosmology- and string-minded physicists; if any of the above challenges are to be fruitfully addressed, it will likely be the result of precisely these sorts of mind-opening interactions, as well as the collaborations to which they merrily lead."

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Volker Mehrmann, Institut fr Mathematik, Technische Universitt Berlin

I happily confirm that the meeting in Banff that I participated was highly fruitful and particularly helpful in my current research. During that meeting two major papers that are just being completed were developed a great deal further. Without this possibility and the nice and friendly atmosphere at BIRS as well as the great facilities this would not have been possible.

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Beni M. Sahai, Senior Scientist (Virology), Cadham Provincial Laboratory, Manitoba

I have participated in two research workshops, in 2003 and 2004, held at the Banff International Research Station (BIRS) on the Mathematical Modeling of Infectious Diseases. I found BIRS to be an exceptionally well-organized and suited venue for holding workshops and research meetings that aim to achieve intensive interactions among participants under highly personable and serene atmosphere. Consequently, meetings at BIRS lead to lasting impact as evident from new research collaborations and scientific publications generated based on such collaborations (for example, see: Gumel et al., Modelling strategies for controlling SARS outbreaks, Proc Royal Society Series B, 2004; 271:2223-32; and current ongoing collaborative research on influenza by our group). I therefore strongly support the renewal and maintenance of this one-of-a-kind international resource.

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Christian Krattenthaler, Institut Girard Desargues, Universit Claude Bernard Lyon 1

I participated in the Workshop ``Recent advances in algebraic and enumerative combinatorics" at BIRS in May 2003.

The workshop brought together participants from different fields having interactions with combinatorics. Thus, in the talks, one was confronted with ideas that one would not usually see at a ``normal" Combinatorics Conference.

I still remember the stimulating atmosphere among the participants during the workshop. There, I had my first encounter with Persi Diaconis. Indeed, he gave me several extremely useful hints and references regarding the paper of mine that I presented (Asymptotics for random walks in alcoves of affine Weyl groups) and another one (Watermelon configurations with wall interaction: exact and asymptotic results).

On a personal side, I also appreciated very much the arrangement that one is next-to-door to artists, myself having been a pianist ``in my previous life".

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Mayer Alvo, Department of mathematics and Statistics, University of Ottawa

As Chairman of the Department of mathematics and Statistics at the University of Ottawa I had occasion to attend a meeting of Chairs of Mathematics at BIRS in 2003. It was beyond doubt of the best facilities for a meeting. The staff was very professional and the accommodations superb to say nothing of the wonderful setting in Banff. Our meeting went extremely well as we had a chance to interact in a quiet environment, un-encumbered by the hustle and bustle of city life. The participants were able to the discuss various subjects freely at different hours in the day. The facilities at BIRS are to be envied and should be preserved. They serve as a model in Canada and no doubt elsewhere in the world.

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Uwe Beuscher, W.L. Gore & Associates, Inc.

This letter is in support of the Banff International Research Station (BIRS). I have participated in a workshop at BIRS in 2002 and have enjoyed it beyond my expectations. The facilities were outstanding and provided a wonderful environment for a stimulation exchange of ideas and discussions well beyond the daily schedule. The unique setup at Banff encourages interactions from early in the morning at the breakfast table until late at night. The staff is very helpful and forthcoming and the facilities were well prepared. I am still benefiting from the connections that were made during the workshop almost two years ago. A follow-up workshop is planned for this March and I would not dare to miss it. Thank you for providing such a wonderful facility and I wish you all the Best for the future.

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Jean-Charles Grégoire, Institut National de la Recherche Scientifique, INRS-Energy, Materials and Telecommunications

I am quite grateful for the flexibility and the quality of the environment provided bu BIRS. For my first experience, it was an opportunity to participate to a gap-bridging meeting which has led me to start research work with a new partner in a complementary discipline. The BIRS formula allows organizers to take more chances in attendance-mix, which may in turn lead to new research perspectives on old problems. I do hope BIRS will be able to expand its programme.

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Joseph Wolf, Department of Mathematics , University of California-Berkeley

I was a participant in the PIMS program on locally finite Lie algebras at the end of Summer 2003. The program was very valuable for me, because the area was moving rapidly and communication between researchers was very much needed. It was needed especially by those of us whose work is not strictly algebraic and who consequently had not been able to keep up with latest developments. Also, I was very much impressed by both the organization and the facilities; definitely a first class operation. The net result of this fine infrastructure was that most of the lectures were very much to the point and most of the free time was devoted efficiently to scientific interchange.

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Jan Zwicky, poet, Department of Philosophy, University of Victoria

BIRS has indeed been exceptionally stimulating for me. I attended a workshop on mathematics and creative writing, and made a number of new contacts that have since provided me with superb leads for my own research. Indeed, a whole new area of research has opened up for me as a result of my participation, and I am extremely grateful for this. The workshop also provided me with an opportunity to present my work to mathematicians, and I found their keen interest both surprising and inspiring.

I hope very much that BIRS will be able to expand its operations to 48 weeks per year.

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Yoshihiro Tonegawa, Associate professor, Department of Mathematics, Hokkaido University, Japan

I participated in the summer one-week program 'defect and their dynamics'. There, I saw Chun Liu from Penn State Univ. whom I knew from the time at graduate school but whom I had not kept contact. After hearing my talk, he started talking about some applications of my result to what he had been interested in. The contact has resulted in our present collaboration of phase interface motion which has both surface tension and hydrodynamic effects. We have been working on some other projects as well, such as approximating Wilmore functional using the phase field approach. This contact has been particularly valuable for me.

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Kyewon Koh Park, Department of Mathematics, Ajou University

I have participated the Workshop on Joint Dynamics organized by D. Lind and D. Rudolph, June 29 - July 3, 2003. It was a great opportunity to meet people in the field, specially young people. I invited one of them to Korea and hope to have a joint work with him.

In Korea, we have right now great possibility of establishing the first mathematics institute. The experience at BIRS was so great that I gave the name BIRS to the Ministry of Science and Technology of Korea as one of the few places to benchmark for our Institute. I hope that we will visit the place again to learn how it is run.

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George Karakostas, Department of Computing & Software, McMaster University

I participated in a BIRS workshop this past summer (CAAN 2004). As a result of the workshop connections, we managed to put together a MITACS project, based on the common experience and research expertise of some of the participants. This proposal has already been forwarded to the current funding decision phase of MITACS, and it wouldn't exist if not for the interaction at BIRS.

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Greg Stinson, Astronomy Department, University of Washington

As a young scientist, my experience at BIRS was invaluable. I attended my first meeting on galaxy formation with all the astronomers who will possibly be colleagues for the rest of my career. I didn't come close to understanding every talk, but in hearing all of the key words, I found out what I need to know the next time I attend a conference with my peers and have done several talks in my department on those subjects so that I could learn what was being discussed at the Banff meeting. I met several of the luminaries in my field and now when I look at articles, I can attach faces to the names of some of the authors and the material seems somehow less intimidating.

All of this learning was made more comfortable by the outstanding setting. I still (one year after the meeting) recall fondly the single rooms with internet terminals and comfortable beds, though I am still perplexed by the two button toilet. The meals were outstanding and I got the chance to meet just about every meeting participant on a more casual level and talk about such random topics as shopping in Germany.

I will also admit that I attended another meeting this past September in Aspen. While the rooms were big and the aspen trees turning, I found that the experience did not measure up to Banff in scenery and in the necessity to go to town for meals rather than enjoying food right on the institute campus.

Banff was a wonderful experience that will always hold the special place of being the first meeting I attended and I look forward to my next chance to attend a meeting there.

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Jim Little, Department of Computer Science, University of British Columbia

I was lucky enough to be invited to a BIRS meeting: Mathematical Image Analysis and Processing Dates: October 23 - 28, 2004 Organizers: Mary Pugh (University of Toronto), Selim Esedoglu (UCLA), Sung Ha Kang (University of Kentucky), Jackie Shen (University of Minnesota)

I am at best a user of the mathematical results of those in the workshop, at least recently, but enjoyed the talks at the meeting immensely. I found an excellent mix of more theoretical and more applied mathematicians as well as some practitioners of computer vision, my speciality. I met several people whose papers I had read, and as well made contact with Andrea Bertozzi of UCLA who shares an interest in mobile robotics with me. Finally I gained a renewed appreciation for the foundational work that these mathematicians are doing in an area close to my research.

BIRS itself as a site is terrific - beautiful, austere but close to the pleasure centre of Banff, and reasonably accessible. A great experience and one I'd repeat again gladly.

I hope to put together a proposal for a workshop in the near future in my area, too.

PS if you need any amplification of this please feel free to contact me.

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David Rocke, University of California-Davis

I attended a statistical genomics workshop in the summer of 2004 at BIRS, and found it an exciting, useful meeting. Several research collaborations have resulted from this meeting, and I plan to attend additional ones in the future if the opportunity arises.

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Peter Jagers, Chalmers University of Technology

I participated in the BIRS week about stochastic processes in genetics in August 2004.

Technically this was a very well organized event. But content was the most important. I met with new problem areas, in particular about fitness evolution, and the intersection between genetics and population dynamics in general, For lack of time this has as yet only resulted in my carrying around a bunch of papers in my back pack, but I am convinced that new insight into the important area of biological evolution will come out of this week, through my research or other peoples.

BIRS is ideally suited for such events which are cross-disciplinary, but still on a high and strict scientific level.

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Henk Broer, University of Groningen

In 2003-2204, during a sabbatical year I visited the Banff Center for a workshop on symmetry in life sciences modelling, coordinated by Martin Golubitsky and Bill Langford. I enjoyed the meeting a lot and learned about all kinds of modelling: in population dynamics, genomics, etc. It motivated and stimulated me to carry on with my own life science program, which now contains 2 PhD students. In particular I was able to make contacts I would not easily have found otherwise.

The scientific environment is extremely good, including lodging and computer facilities. Also, the Rockys are very pretty, not to mention the elks. I think the place is quite comparable to the European setting of Oberwolfach.

I wish you good luck with the continuation !

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Peter Schneider, Mathematisches Institut, Universitt Münster

so far I have participated twice in workshops at the Banff center. But the first time was before the BIRS had its own housing. The second time was in the summer of 2003. Both workshops were a very useful and inspiring experience for me. I grew up here in Germany mathematically in the tradition of Oberwolfach. The conferences and workshops there have contributed to my mathematical development in a way which can hardly be overestimated. It therefore has always struck me as quite odd that there existed no equivalent to Oberwolfach (and Luminy since 1981) in North America. I'm truly convinced that the BIRS now provides such an equivalent. Such places are invaluable. In a relaxed and inspiring atmosphere they foster research through the intensive exchange of ideas. In addition the workshops are an indispensable tool in the training of young mathematicians. Due to the geographical distance it is obvious that places like Oberwolfach or Luminy located in Europe cannot fulfil these purposes in a satisfactory way for mathematics in North America. To me it therefore seems crucial that the BIRS will be able to continue functioning and possibly will even expand its activities.

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Terry Lyons, Mathematical Institute, University of Oxford

In my experience, these meetings, and the environment are fantastic. I feel privileged to have participated. They have stimulated my mathematics and increased my scientific motivation. Through contacts with colleges I have been able to use their expertise directly in my research.

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Moty Katzman, University of Sheffield

My recent stay at BIRS had very tangible effects on my research. The ability to interact informally in such a wonderfully peaceful setting with colleagues in my field enabled me to learn about the problems they were tackling, to show my own work and to benefit from their feedback and collaboration. For example, I have learned from my colleagues in BIRS that a problem I had been thinking about for some time is related to one which was studied in the early 80's and I learned from my colleagues some techniques which might crack it.

While it is hard to pinpoint all the benefits from the meeting in BIRS, I have no doubt that they are very considerable and will impact my research. I look forward to my next visit to BIRS!

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Norman Dancer, Justus-Liebig-Universitat Giessen

My visit to BIRS was very productive.The meeting was very well organised with a quite diverse group of mathematicians attending.I learnt a good deal on other approaches to problems in related areas. In particular,my work was considerably influenced by a discussion with Schatzman.This influence is on work which is continuing and some of this will be eventually submitted for publication.

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Nancy Amato, Professor, Parasol Lab, Department of Computer Science Texas A& M University

I participated in a BIRS workshop in July 2004 on modeling Protein Stability, Flexibility and Motions. It has been extremely useful for my research. I think the most important aspect for me was to get a chance to spend serious time talking with researchers from other disciplines - this is just not possible in most other settings. In fact, all my interdisciplinary collaborations that are not with researchers at my own institution grew out of such interactions (week long workshop settings). Although it is a bit early to say for sure given that it was only a few months ago, I believe a multi-disciplinary collaboration between me (a computer scientist), a mathematician and a biophysicist will grow out of the BIRS workshop I attended. I also found it very beneficial to be able to bring one of my graduate students to the workshop - I know she was thrilled to spend that much time with senior researchers in other disciplines.

Please let me know of anything else I could do to help keep BIRS around. I think it is a wonderful resource and I would be happy to do what I can.

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Merel Soons, Landscape Ecology Group, Department of Geobiology, Utrecht University, The Netherlands

I would like to let you know that the workshops and small-group working groups at BIRS offer a unique opportunity to really get to work. The facilities at BIRS are optimized for carrying out simulations, analyzing data, having discussions, and writing papers (as opposed to almost all other places, which usually only facilitate having discussions). Thus, meetings at BIRS are much more productive than meetings elsewhere. I have experienced this myself and left a BIRS workshop with one paper partly written and others under way.

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Hans-Otto Walther, Justus-Liebig-Universitat Giessen

being one of the organizers of the workshop on Functional Differential Equations (November 6-11, 2004) it is my pleasure to emphasize that BIRS and the Banff Centre are an ideal place for smaller meetings which concentrate on top research and are open to promising young scientists. A characteristic of the workshop on FDEs was perhaps that it brought together several people who had known each other's work before to some extent but not very intensely; the workshop led to a much better understanding. This refers in particular to the relationship between purely mathematical results and applied work (mostly in nonlinear optics, molecular biology, population models).

As a consequence of the workshop I began to work with a colleague in physics on aspects of a degenerate bifurcation problem (part of a Takens-Bogdanov scenario) which I had not touched before (asymptotic expansions). Also discussions at the workshop with a colleague in mathematical biology and with a further colleague, about fundamental problems for equations with state-dependent delay and a more functional analytic approach, may lead to closer cooperations. A Ph D student of mine who attended the workshop used the opportunity to meet the experts in the area and to make his work known.

It is important for mathematics to have research centers like BIRS - and pleasant. There are not many of these worldwide, so I do hope that your efforts to continue and extend the operation of BIRS are successful.

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John Glasser, Centers for Disease Control and Prevention, USA

I participated in two infectious disease modeling workshops during 2003-04, and have agreed to participate in another next summer.

I am collaborating with a colleague whom I had only met briefly before the first of these. She will present some of our work next summer, by which time we hope that it will be in press. Internal review at the Centers for Disease Control and Prevention (CDC) can be painfully slow.

I have either discussed, or planned collaborations with others whom I met at the BIRS. I have presented some work at the Center for Discrete Mathematics and Theoretical Computer Science and Mathematisches Forschungsinstitut Oberwolfach, and plan to present other work next summer.

Colleagues and workshops on infectious disease modeling are invaluable to me, as I am the only mathematical epidemiologist at the CDC.

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Dan Zuckerman, Center for Computational Biology and Bioinformatics, University of Pittsburgh

The workshop I attended on protein flexibility was extremely valuable. I am a physicist who now works on computational biology, but I was very much in the middle of the spectrum (from math to biology) at the workshop, and I learned from both ends. There were top experimental structural biologists at the meeting who clarified many key points regarding the structures on which we simulators rely so heavily (too heavily, as it turns out!) and the mathematicians there taught me to think in terms of rigidity and constraint-counting. It is the best workshop I have attended.

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Matthew Emerton, Mathematics Department, Northwestern University

I'm writing in response to your email regarding the upcoming application for renewal of support for the BIRS.

In August 2003 I attended the workshop ``Current trends in arithmetic geometry and number theory''. The workshop offered a mixture of research and instructional talks, both of which were of the highest quality. Furthermore, I found that the BIRS setting of the workshop encouraged fruitful collaborations and discussions outside the formal setting of the talks. In particular, during the week of the workshop, my collaborator Robert Pollack and I were able to make substantial progress on a joint paper. This paper, ``Variation of Iwasawa invariants in Hida families'', written jointly by Robert Pollack, myself, and Tom Weston, is now completed and has been submitted for publication.

I was one of the organizers of the workshop ``p-adic variation of motives'' in December 2003. Unfortunately, for personal reasons I was unable to actually attend this workshop. However, after it was over, I received email from several people, including Adrian Iovita and Jacques Tilouine, describing the workshop as ``really good'' and ``important''.

Overall, my experience shows that BIRS plays an important role as a host for mathematics workshops at the highest level, and I wish you the best of luck in having its funding renewed.

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Angele Hamel, Wilfrid Laurier University, Alejandro Lopez-Ortiz, University of Waterloo

We organized a two day workshop, Combinatorics and Algorithms for Networking and the Internet (CAAN04), at BIRS from August 5 to 7, 2004.

BIRS was a major reason for the success of our conference. In fact we agreed after the workshop that BIRS and the Banff location was what made the difference between our conference just merely succeeding and succeeding well.

The staff were helpful and organized, both before and during the conference. They made our job easy. The facilities were all we could hope for, from the technology in the lecture rooms, to the accommodation, to the food and conveniences provided in the lounge. The proximity to Banff was a definite plus. We received numerous compliments from the participants on how wonderful the setting was.

From a scientific point of view the workshop was also a success. In one of the talks the presenter proposed a solution to a major outstanding problem in the field and there is now ongoing work to further evaluate the correctness of the solution. The Springer-Verlag series, Lecture Notes in Computer Science (LNCS), has expressed interest in publishing a volume dedicated to the workshop and consisting of the presented papers along with a number of invited survey papers. We anticipate that this volume would become a standard reference or graduate text in this emerging field. One of the most valuable outcomes of the workshop is the provision of a summary of the current research directions in this rapidly changing field. New collaborations are another possible outcome of the workshop. There was clear interest among the participants for further discussions and collaborations, although the interaction of the participants was somewhat limited by the short duration of the two-day format.

On the strength of the success of this workshop, we are planning to organize a follow-up workshop, CAAN05, as a satellite conference of the Workshop on Algorithms and Data Structures (WADS05) to be held in Waterloo, Ontario in August 2005.

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Francisco Marcellan, Professor of Applied Mathematics, Universidad Carlos III de Madrid

As a participant in the BIRS meeting on ``Integrable Systems and Orthogonal Polynomials" held in Banff in March 2004 I would like to recognize the important consequences of my participation in terms of my research activity. First, I met there the top researchers in my area of interest. As a consequence, I was able to contact directly with them as well as to learn about the last research directions. Thus, new ideas for a future work were introduced and I hope I will able to do something with some of them in the next coming time. Second,the friendly atmosphere as well as the excellence of the facilities, which constitute a reference in the world community of mathematicians must be emphasized. Your example shows how good conditions yield good results and I would like to use your experience for our proposal of a research mathematical center in Spain. Finally, I would like to stress my support to the activity of the Pacific Institute for the Mathematical Sciences.

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Gloria Mari Beffa, Mathematics Department, University of Wisconsin

I participated in a meeting at the Banff international research center two years ago, a meeting on the Theory of differential invariants and its applications (this is not the exact name, I am sure) organized by Niky Kamran and Peter Olver. The meeting was meant to bring together researchers in the theory of differential invariants (I study the geometry behind) and applied researchers who use it for their study. It was meant to bridge the traditional separation between both groups.

I think the meeting was a big success, at least from my own personal point of view. I met many applied mathematicians and I learned a lot about how the math I do is connected to interesting applications. After the meeting I had many quite long e-mail interactions with Professor Harvey Segur (from the Applied Math Department at the University of Colorado at Boulder) and learned a lot from them. He answered many of my questions and I tried to answered his. I also got introduced to the subject of image processing and the application of differential invariants to the design of image enhancing. After the meeting I became the unofficial consultant of the image processing group here at the University of Wisconsin, a group that consult with me about geometric problems. In particular I advised a graduate student in Engineering about integral invariants and its applications. The student wrote a very successful code for face recognition based on integral invariants and they are pursuing a patent for it. I believe the meeting in Banff had a lot to do with whatever interaction I have with the applied community.

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Vince Carey, Assoc. Prof Med (Biostatistics), Harvard Medical School, Channing Laboratory

I was a participant in the BIRS Workshop ``Statistical Science for Genome Biology" in August 2004. This workshop brought together statisticians, computer scientists, and bioinformaticians for a structured program of lectures on various aspects of statistical inference in genome science.

The setting and program generated protracted discussions and after-hours work by subgroups. I had no way to anticipate the ideal nature of the arrangement. The meeting brought to my attention work on a variety of topics that might otherwise not have been encountered: contributions from computer science to the evaluation of multinomial likelihood statistics; new bayesian approaches to sequence alignment.

I strongly endorse any plan to offer this opportunity to a wider population of researchers.

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Don Dawson, School of Mathematics and Statistics, Carleton University

I am very pleased to support the renewal proposal for BIRS. I participated in two five day workshops during 2003-2004, first as participant and second as co-organizer of the workshop on ``Stochastic processes in evolutionary and disease genetics". In both cases the workshops were of the highest quality. The Banff setting is ideal for an intensive five day workshop and the facilities are excellent. This type of workshop is particularly valuable in bringing together researchers from related but different disciplines to focus on a research challenge at the boundary of these disciplines. In my capacity as co-organizer I was impressed by the exceptionally high rate of acceptance of invitations to participate and the many other expressions of interest in the workshop that we received.

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Gerardo Emilio Garcia Almeida, Facultad de Matematicas, Universidad Autonoma de Yucatan, Mexico

I participated recently in a 5-Day Workshop at BIRS. This workshop was on mathematical image analysis and processing and it was an excellent opportunity to contact people doing research on this area. Here in the Faculty of Mathematics, Universidad Autonoma de Yucatan (Merida, Yucatan, Mexico) there is a group of mathematicians (me included) and computer scientists interested on this research area and we have a weekly seminar on this topic. After the workshop I commented them about the topics discussed in the workshop and showed them a video of one of the talks. Now we have a better idea how Mathematics can be applied for image processing and computer vision. We've had this seminar for a year and at the beginning for the mathematicians it was no clear how different branches of Math like Differential Geometry, Mathematical Analysis and Function Spaces are used for image processing and computer vision. On the other hand, people from Computer Science didn't have a deep knowledge on those areas of Math. It's very likely that with the information I learned, the videos I recorded of some of the talks, and the contacts made in that workshop we will be able to contribute to this fascinating area of Applied Mathematics soon.

Needless to say, I found the infrastructure and support from staff at BIRS superb. I'm glad to know that you are planning to extend your operations to more weeks a year. In my opinion, this kind of ventures are very good for the development of the Mathematical Sciences and should be supported.

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Dirk Becherer, Department of Mathematics, Imperial College London, South Kensington Campus

I have visited the BIRS in summer 2004, and enjoyed an excellent workshop on mathematical finance. I do find such 'Oberwolfach Style' small workshop research stations extremely helpful, as they provide a young researcher with new contacts and the opportunity to get to know other people in their research field. For instance, I have met Tom Hurd who is working in my research area for the first time, and I did also discussed with Thaleia Zariphopoulou. The latter helped in preparing the ground for my 2weeks visit at her University in Austin, Texas. Furthermore I met further younger researchers whom I did not even knew about before, but who work in my interest areas (eg Simon Brendle from Princeton).

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Karin Melnick, Department of Mathematics, University of Chicago

I attended the workshop on New Techniques in Lorentz Manifolds in November 2004. I am a fifth-year graduate student at the University of Chicago, and this was my first conference.

The workshop was great. The small size-there were about 25 participants-meant that, even as a graduate student, I was able to meet and talk with everyone. I made many good contacts, particularly with people from the Ecole Normale Superieure in Lyon, France, where I will be visiting next spring.

The setting was also very good for my first conference talk. Again, because of the small size, the atmosphere for talks was comfortable and informal, and everyone attended essentially all the talks.

It was an all-around fantastic experience to be at BIRS for five days. I appreciate having had the opportunity to go, and I hope that you will continue-and perhaps expand-your programs there.

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Steve Giddings, Department of Physics, University of California-Santa Barbara

I have been a coorganizer both of BIRS' first workshop, in 2003, and of a workshop in 2004.

In my opinion BIRS supplies a fantastic format for collaborative discussion and research. In our first workshop we were a little uncertain how to optimally organize things, but in our second we feel we `got it right' and had a very stimulating, interesting, dynamic, and fun workshop. We heard a number of very positive comments from our participants, and feel that it catalyzed important discussions and further research.

In particular, the BIRS configuration, where all the logistics are taken care of so people can focus on science, is really a great idea.

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Walter Whiteley, Professor of Mathematics and Statistics, York University, Director of Applied Mathematics, Member of the Graduate Programs in Mathematics, in Computer Science, and in Education

In July 2004, I was a participant in, and an organizer for, an interdisciplinary BIRS workshop on Modeling Protein Flexibility and Motions. This workshop was an exceptional gathering of people from mathematics, computer science, biophysics and biochemistry, with diverse points of view on a set of shared problems. Both the support of this site, and the exceptional nature of the setting contributed in an essential way to our ability to gather a range of participants from world leading experts to graduate students. This was not a group that would have met under other circumstances, but the exchanges were so rich that we have strong hopes to meet again in a couple of years. The workshop also generated a web resource, at http://biophysics.asu.edu/banf/list.php, which continues to be a resource for researchers and students who are working in this area.

The workshop (and a 2 day extension at the University of Calgary), generated a number of promising unsolved problems, proposals for comparisons of theory and data, conjectures for specific work, and new collaborations. I am personally involved in two writing projects which will present new mathematical and modeling results which arose out of the exchanges around the workshop. There are work with some of my graduate and undergraduate research students here at York which is implicitly a response to queries and confusion which came up during the exchanges. I should say the exceptional wireless access throughout the workshop enabled significant sharing of resources, almost on demand, morning and evening, as the workshop proceeded.

To support our interdisciplinary work, and a number of other ongoing collaborations, I have a number of additional resources to call on. I am now much freer to propose projects for my graduate students, knowing that I can tap into the state of the art information to start them off in the right direction. These contacts are invaluable, and the overview developed from the workshop helps us all to sort out the significant questions from those which have been answered, or are known to be dead ends. Such an overview may be intangible, but it certainly is of primary significance in an area of rapid development and of new collaborations.

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Claude LeBrun, Professor of Mathematics, SUNY Stony Brook

I attended last summer's workshop on conformal geometry, and thought it one of the most stimulating conferences I'd attended in recent years. The conference managed to bring together folks from quite different mathematical disciplines, and, as a consequence, people were proving new theorems, right-and-left. The venue was remarkably beautiful and stimulating, and I left feeling really invigorated -- and with enough new material in my head to write several papers!

I sincerely hope that funding for the BIRS will be renewed. It is an institution of which Canadians should feel extremely proud.

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Katie Pollard, Postdoctoral Researcher, Center for Biomolecular Science & Engineering, University of California-Santa Cruz

I participated in the BIRS workshop ``Statistical Science for Genome Biology" in August, 2004. This week was a fabulous experience for me professionally. One year into my postdoc, it was an opportunity for me to get to know professors and students from several leading programs in my research area. These connections have led to my applying for two faculty positions that I might not have otherwise considered, one of which has already resulted in an interview! I also learned about a good, small conference in my research area that I hope to attend next year. In addition, a discussion at BIRS has sparked a new research collaboration. Finally, the week also provided me the opportunity to reconnect with several colleagues I already knew (from graduate school or other conferences) as well as meeting several people I knew only by name before BIRS. The setting in Banff, as you know, really encourages interaction beyond that of a typical conference.

This was my first experience at BIRS and I certainly hope to be back again in the future. In fact, I was so excited after the workshop in August, that I am a co-organizer on a new application for a workshop in 2006.

Thank you for a wonderful and unique professional gathering!

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Marjorie Wonham, Centre for Mathematical Biology , University of Alberta

I am writing to express my appreciation of the two BIRS workshops I attended in 2003-2004 (Mathematical Biology: From Molecules to Ecosystems: The legacy of Lee Segel BIRS Workshop July 5-10, 2003 and 2-day Retreat on Mathematical Ecology and Evolution March 25 - March 27, 2004).

As a field biologist by training, I have come recently to mathematical biology as a postdoc, and have found collaborative events such as these workshops very influential in exposing me to new ideas and introducing me to new colleagues. At the Lee Segel workshop, I presented - with a certain amount of trepidation - my first modelling work, on West Nile virus. I was delighted by the constructive and helpful feedback, and it definitely improved our subsequent paper (Wonham et al. 2004 Proc. R. Soc. London B)

The second workshop was a student oriented event where we brainstormed new project ideas introduced by graduate students. I thought this was a terrific model for helping students develop their ideas with the focused attention of colleagues they might not otherwise encounter in their home institutions. Creativity, insight, and good humour abounded - it was inspiring and energizing.

In my admittedly limited experience, the BIRS atmosphere seems to be one of openness, collaboration, and collegiality - not to mention smooth logistics, excellent food, and great access to the mountains. The model developed for mathematical biology would extend naturally to other disciplines - my only reservation is that this might reduce my chances of returning for another math biology workshop!

Congratulations on making BIRS a super place. I'm looking forward to an opportunity to return.

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Eckart Viehweg, University of Duisburg-Essen, Germany

In the development of mathematics in Germany the Institute in Oberwolfach played an important role. In a decentralized Country the existence of an international conference center has an extreme impact on the development of the research in the field. When I visited the Banff International Research Station one year ago, for the first and only time, for the conference on ``Calabi-Yau Varieties and Mirror Symmetry" I realized, that this Institute tries to be some ``Oberwolfach" for the Canadian mathematical community. No a copy, perhaps a more modern version (and the landscape is more impressive and the food is better).

Being able to participate in the workshop was extremely stimulating for my research. Coming from algebraic geometry, it was a unique possibility for me to meet differential geometers, and physicist working on mirror symmetry, and to put my own work on moduli of Calabi-Yau varieties in the framework of a more general picture. Necessarily this contact influenced the direction of my research afterwards, and at least two articles ``in progress" have benefited from the workshop.

For me it was the first visit to Canada for mathematical reasons, (although I had a lot of contacts to Canadian mathematicians before) and after the success of the workshop I am sure it will not be the last one.

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Nobuo Hara, Mathematical Institute, Tohoku University

I am writing to reply to your request on support for BIRS. I have participated in BIRS workshop ``Commutative Algebra: Homological and Birational Theory" held in the period of September 11-16, 2004. There I knew interesting new results and had nice discussions with some participants including L. Ein, M. Hochster, P. Monsky and V. Srinivas. Actually, I encountered the new notion of ``p-fractal" in Paul Monsky's talk in the workshop, which enabled us to start a joint work that is now going on. Also, I could have a few-hour stimulating discussion with Lawrence Ein after a session. I hope that these experiences of mine give an evidence how excellent environment BIRS provides to mathematicians.

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Simon Guest, Department of Engineering, University of Cambridge

I attended the workshop, 'Modeling Protein Flexibility and Motions' at the Banff International Research Station in July 2004. I am very happy to write in support of the work of BIRS, because I thought this was the best workshop that I have ever attended. Part of this is due to the workshop organisers, of course, who brought together a tremendously exciting cross-disciplinary group of academics. But in no small part it is due to the environment that BIRS provides. The arrangement of accommodation, social areas, lecture rooms, printing and computer support, catering, and the physical environment, all led to an ideal stage for academic discussion.

There is no doubt that BIRS is providing an exciting resource to the mathematical community, and the wider academic world. I have no doubt that, if BIRS is able to continue and flourish, there will in future years be many academic breakthroughs that trace their ancestry to a workshop at BIRS.

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Robert Bridson, Department of Computer Science, University of British Columbia

I attended the Pacific Northwest Numerical Analysis Seminar at BIRS back in October, where I had a great opportunity to get back into numerical linear algebra--meeting my old advisor again, getting into talks on the subject. Chen Greif and I had been discussing an idea I had earlier about a generalization of Krylov methods, and the stimulating company along with simply being in a great environment for thinking (away from departmental distractions) helped us turn this into a paper we just submitted to SIMAX.

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Paul Van Dooren, Centre for Systems Engineering and Applied Mechanics, Universite Catholique de Louvain, Belgium

I have participated only once in a workshop at the Banff International Research Center (Model Reduction Problems and Matrix Methods, April 3-8, 2004) but is was a fantastic meeting.

The organizers had chosen a timely topic and invited the experts in the area. It was a very stimulating conference in which all the talks were attended by almost all participants. The numerous discussions resulting from the presentations clearly showed that new ideas were emerging from the interactions at that meeting.

On top of that I'd like to mention also that the infrastructure is great. The rooms and conference rooms are very well equipped (computer access, printing facilities, audio-visual equipment were first quality) and the personnel was very helpful.

It was a memorable event.

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Rodney Y. Sharp, Department of Pure Mathematics, University of Sheffield

A few weeks ago, I was fortunate to be an invited participant at a workshop at the Banff International Research Station for Mathematical Innovation and Discovery (BIRS). I understand that BIRS is administered by the Pacific Institute for the Mathematical Sciences (PIMS), and I am writing to you, in your role as Director of PIMS, to express my appreciation of the facilities provided at BIRS.

The workshop which I attended provided excellent opportunities for serious mathematical discussions between individual participants, because there were adequate gaps between the scheduled talks. Indeed, I observed several pairs of participants in lengthy and detailed discussions about collaborative research. I myself benefited not only from discussions with other participants, and consolidation of important contacts, but also from several of the inspiring lectures given by experts present at the meeting.

I would also like to compliment the PIMS management on the practical arrangements provided for workshop participants at BIRS. In addition to the large lecture theatre, several smaller rooms were available for use by small groups (or even just by two people wishing to discuss their collaborative research); the living accommodation, with computer terminals in the bedrooms, was very good, and the informal breakfasts worked well; the lunches and dinners in the Banff Centre Dining Room were really excellent. In addition, the transport links, the surroundings, and the beautiful scenery in the neighbourhood, are even better than those at Oberwolfach. All in all, BIRS is an excellent facility for the international mathematical community.

If I am ever invited to another workshop at BIRS, I shall do my very best to attend!

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Rene Boel, Ghent University, Belgium

I participated this year in the ``Banff DES Workshop" on May13-15. This was an extremely interesting workshop thanks to the very clear focus on complexity of large DES systems control, and the possibilities of hierarchical and (most interesting to me) distributed approaches. The workshop provided the opportunity to discuss very intensely during a short time span of only 3 days these problems with a number of people I already knew very well beforehand (Lafortune, Ricker, Caines, Sreenivas), but it also led to discussions with researchers I got to know much better in Banff (Thistle, O'Young, Romanovsky, Mallon). We had very interesting discussions on one particular topic, decentralised observation and fault detection of large DES, that helped me and my Ph.D. student to refocus our work. Some of the discussions led to ideas on possible ``test cases" or ``benchmark problems" that we all try to solve, and this exchange of benchmark problems will certainly help in better understanding the relations between the different approaches we use to solve the same (or at least very similar) problems. I have discussed this work by e-mail, and at two later conferences (MTNS in July 2004, WODES in September 2004), with several of these people. We have not yet written down our common thinking in joint papers, nor have we managed to set up common research projects (the distance between Europe and Canada is still rather large I am afraid!), but certainly this Banff Workshop has brought us closer together. To me it has been for me a very enriching experience. It has influenced my research topics, and the work of one of my Ph.D. students, in particular by convincing me of the need to study concurrency problems in a model independent way (rather than the Petri net based approach I used in the past). As a European I certainly believe this has been a very worthwhile experience for the Canadian researchers, and I would hope that

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Sean Sather-Wagstaff, University of Nebraska-Lincoln, USA

I had the privilege to participate in the workshop on ``Commutative Algebra: Homological and Birational Theory" at the Banff International Research Station (BIRS), September 11-16, 2004. It was a fantastic experience. The facilities at BIRS are top-notch. Each sleeping room is clean and well-furnished and has its own workstation. The coffee room was nicely furnished and always well-stocked, though it would be great to have some white or black boards to work on. The lecture room was well-constructed, with good board space and computer hook-ups. And the dining facilities made our meals wonderful.

The atmosphere at BIRS is of the highest quality. The workshop, in my opinion, was the model for workshops. Not only were there many interesting talks, but there was ample time (and space) for participants to discuss mathematics outside the lectures. Personally, the conference brought me in contact with people I normally wouldn't meet, with one consequence being the proof of part of a conjecture I have been thinking about for some time now. Too often, conferences and workshops consist of talks with no time between for the participants to actually work, which defeats half the purpose of bringing researchers together. The people at BIRS should be applauded for getting it right. Housing and feeding everyone together made the workshop even more intimate and gave us even more time to work together. Much praise should be directed at the people who run the conference center, as the week came together seamlessly.

BIRS is a fantastic place, on par with the CIRM in Luminy. I very much hope to be able to participate in other workshops there in the future.

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Patrick Speissegger, Department of Mathematics and Statistics, McMaster University

I profited from participating in the workshop ``Interactions between model theory and geometry", which took place March 13 - 18, 2004, in two ways: first, I witnessed a conjecture of Anand Pillay's on a descending chain condition for groups definable in o-minimal structures being proved at the workshop; a paper summarizing the result has been submitted for publication by the four collaborators involved. Second, working together with Jean-Philippe Rolin, another participant at the workshop, we started a new project where we intend to study the expansion of the real field by certain classes of functions appearing in, and crucial to, Il'yashenko's proof of Dulac's Problem concerning limit cycles of planar analytic vector fields. To be free from the usual distractions of the home institution, as was the case during the workshop at BIRS, made it possible for us to come up, within just a few days, with a possible direction and some first rough ideas for this project.

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David Kutasov, University of Chicago

I attended a workshop on string theory at BIRS in the winter of 2003. This was a very useful experience. I met many people I normally wouldn't, and got the idea for a paper that was published a few months after the workshop, as hep-th/0304045, Nucl. Phys. B666 (2003) 56-70. I hope the important work of BIRS will continue to be supported by the funding agencies.

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Anatoliy Swishchuk, Mathematical and Computational Finance Laboratory, Department of Mathematics and Statistics, University of Calgary

I've recently participated in MITACS Project Meeting: Modelling Trading and Risk in the Market, November 11-13, 2004, BIRS, Banff, AB, Canada.

I've found BIRS as a very nice place to bring academic researchers in mathematical and computational finance together with risk managers and quantitative analysts from industry to share new ideas, practical and theoretical questions of the moment, current research, and to foster closer collaboration.

In this way, BIRS helped me to be familiar with new results in this area, to make new contacts I have not had early and originate my paper ``Modelling and Pricing of Variance Swaps for Stochastic Volaitlities with Delay" during the workshop.

In this way, BIRS is a very useful instrument at the service of the scientific community, a place where research and discussions can be conducted under the best conditions, and I strongly express my support for BIRS.

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Trung Van Nguyen, Department of Chemical and Petroleum Engineering , University of Kansas, 2002-2005 Madison & Lila Self Faculty Scholar, Graduate Advisor

I strongly support the service that the Banff International Research Station has been providing to the scientific communities. I had looked at the programs at the Banff IRS and was surprised and impressed at the programs organized and the level of services provided by this center.

My graduate student and I attended a workshop on Fuel Cell Computational Fluid Mechanics organized by PIMS at the Banff IRS in 2003 and have found it to be a very useful experience. For me the workshop provided great contacts with colleagues working in the area, and for my student it provided a great exposure to what his peers were working on and the challenges of their research area and an opportunity to show and discuss his own his research activities and to establish contacts with his peers.

If I could be of further assistance, please feel free to contact me.

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Chris Mertens, Math Department, Sundre High School

My experience at the Banff International Research Station was in one word, phenomenal. We were asked to present at a conference sponsored by PIMS in May of last year. Our topic was one that we are involved in regarding ``Lesson Study" and ``Math Fair" in a high school setting. We were warmly received and there was great interest for more information about our work. We made contacts with individuals who gave us ideas to improve on our project. If asked to attend another of these conferences, I would not hesitate to say yes!

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Mike Baines, Professor of Applied Mathematics, The University of Reading, UK

Yes, I was a BIRS participant in the summer of 2003 (one of the PIMS workshops). I thought that BIRS was an excellent venue with a fine mixture of intensive study and cross-subject interaction in a stimulating atmosphere. I very much appreciated and benefited from the facilities and the high standard of the workshop. It gave me an opportunity to describe and develop new ideas and bounce them off some big names in my field of the analysis and numerical analysis of moving mesh methods. Without that experience I doubt whether I would have developed my recent work (and of papers) on scale invariant moving mesh finite element methods for partial differential equations, with their properties of following exact solutions so closely.

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Gideon Maschler, Department of Mathematics, University of Toronto

I have participated in a workshop on May 2004 (Conformal Geometry), and am scheduled to attend another one on May 2005. Besides being quite pleasant, my assessment is that it was indeed very useful. The workshop coordinators did a very good job of inviting workers who have not all interacted with one another beforehand. I made many new contacts, and realized how work I have done is related to other work which I was not aware of. At least one topic in the workshop have since become an area of interest for me, and I am trying to produce new results in this subfield. I have subsequently read many papers that I may have not even considered reading, if it were not for the workshop. In short, the new mathematical relations, the intimate nature of the interaction, and the inspiring beautiful environment are benefits that I have not always experienced in other types of conferences and meetings. I strongly support the continuation and renewal of the BIRS.

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Peter Loly, Professor, Physics & Astronomy, University of Manitoba

I returned to Banff this past September to attend the Theoretical Physics Institute (Alberta) Symposium, which included the Donald Betts tribute, many years after I used to attend NATO ASW's and Summer Schools at the Banff Centre.

The event was a reunion in part, and it served to make me aware of the recent changes due to the conception of BIRS, as well as PIMS. This is an admirable facility which I hope to visit again, perhaps as soon as the 2005 Renaissance meeting.

I have to follow up on some unexpected contacts flowing from the meeting.

The residence rooms were very comfortable, and, once I got through a long setup process, well-equipped with computer facilities.

It would have been of some interest to me if there had been some resident mathematicians with whom I might have discussed some of my work which might lead to proposing a future event related to magic squares.

I recommend the BIRS facility as a great place to bring specialist meetings.

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Phill Holmes, Department of Mathematics, Princeton University

I attended the workshop on creative writing in and about mathematics, from 17 April to 22 April, 2004, at BIRS. It was one of the most interesting gatherings I've attended, with a wonderfully heterogerneous group of mathematicians, scientists, philosophers, playwrights, poets, novelists and writers. We did not discuss technical aspects of math, but went further into influences from, implications for, applications to, interactions with the larger world than is normally possible (or desirable). Since I am an applied mathematician and a poet (having published 4 collections), this was perfect for me.

The meeting was structured more like a writers' workshop than a math conference: each afternoon we went off to our rooms, or up the mountain, or to a coffee shop, and wrote or worked on something, which we brought to the following morning session's open discussion. Such composing/researching `in the moment,' was a great experience for me, and got me moving on a recalcitrant poem. I also composed and more-or-less finished a poem which has just appeared, along with some earlier work, in the Mathematical Intelligencer (Vol 26, No 4, 2004). So, I didn't get a theorem out of it, but I did get 2 poems and motivation for several more!

PS. You should already have a note in your files that I wrote to Robert Moody about this workshop.

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Daniel Lenz, Fakultt fr Mathematik, Technische Universitt Chemnitz

let me write to say how much I hope BIRS will continue its program.

I have had the opportunity to attend a workshop this spring. Both the relaxed atmosphere at BIRS and the excellent choice of participants have made this workshop a most stimulating and fruitful research experience. In fact, discussions at this meeting not only helped me with ongoing work but also initiated a new project, which I am currently working on.

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Yvette Mandin-Kelly, Dovercourt Elementary School

I would like to share with you my experience while attending the Banff workshop in mathematical sciences and how it has benefited my students, my school, and colleagues. I am a regular classroom teacher who works with students who have had difficulty picking up on reading and learning math concepts in their first three years of formal schooling. With this comes the challenge for them to also show their understanding by speaking or writing their thoughts and ideas.

Math is something that for a lot of them is something they are just not good at. I have had a passion and commitment to being able to break down concepts and communicate effectively so that they are able to begin to understand concepts, recognize patterns and develop strategies and a positive outlook so they will embrace the challenges of doing math.

I am also very curious and interested on where do certain mathematical ideas start.

A consultant with our school district thought that the workshop would be right up my alley. Well with trepidation of being with 'mathematicians', off I set. I had a terrific time in the sessions, was able to bring the perspective of people who math doesn't necessarily come easily, to use a constructivisionist's approach and to learn, learn and learn with other division teachers, to be inspired by other passionate 'closet' mathematicians and to be able to talk to international math instructors.

It was an experience that I came away with more excitement, energy and fire to share with my students, my staff, colleagues in my ``special needs" field and to lead some hands on workshops with colleagues.

I was also very impressed and appreciative of being able to benefit from BIRS.

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Michael Coelli, PhD Candidate, University of British Columbia

I attended the BIRS workshop on estimation of peer effects in April of 2004. I had the great opportunity of meeting with many scholars in the field, both experienced and new. The workshop itself made me much more aware of the current trend in research in this area, and will shape how I approach my own current research on estimating peer effects. I have also gained from comments given to me by participants about other work I am undertaking that I had the opportunity of discussing with these leaders in the field. The workshop was very influential in shaping my current and near future research.

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Vyacheslav Zaharyuta, Sabanc universitesi, Turkey

I express my gratitude to BIRS for a great success of the conference in Complex Potential Theory. This conference was extremely important for me personally, because I had joint scientific interests with the majority of its participants and in was very useful to discuss with them old and new problems in this area. In some extent such discussions even more useful than talks themselves. It was a great idea of the organizers to invite some specialists from adjacent areas (especially, Rumely, Saff and Totik). For example, it was a great pleasure and surprise for me, that my results of 70ths about the multidimensional transfinite diameters and Chebyshev constants has been used efficiently in the very impressive recent results on Algebraic Geometry (by R. Rumely, C.F. Lau and R. Varley). I hope that it would be another possibility to organize a conference in Complex Potential Theory (maybe jointly with some closely related directions).

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Anne E Henke, Department of Mathematics and Computer Science, University of Leicester

This is to say that I participated at a Banff-workshop last autumn (October 2003). It was a high quality workshop and I was very happy that I got the opportunity to participate. As I come from Europe, the opportunity to present my work to an American/Canadian audience, was vital to form new contacts. In particular in Banff I got into contact with G.Cliff from Canada. As a result, an exchange with a former student of Cliff and myself is planned for next year. I am very grateful for the opportunities and stimulating environment Banff offered me.

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Carlo R. Laing, IIMS, Massey University, New Zealand

I attended the workshop on Symmetry and Bifurcation in Biology at BIRS in 2003. It was an opportunity to present my work to very interested audience, something that does not often happen at conferences with much broader audiences. I gained a lot from the meeting, and enjoyed the opportunity to spend time with other people working in my field. I particularly benefited from the ``spare time" between sessions, which I used to talk in more detail with several of the participants about their work and its relationship to mine.

I think BIRS is a wonderful establishment and consider myself very lucky to have spent some time there. I fully support the continuation of BIRS.

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Donna Calhoun, Department of Applied Mathematics, University of Washington

I have been to two BIRS conferences - Moving and Free Interface Problems, (organized by Randall LeVeque and Bob Russell, Aug. 2003), and the Pacific Northwest Numerical Analysis Seminar (PNWAS, organized by Chen Greif, Sept 2004). My experience at both workshops was nothing but positive. The setting is beautiful and provides the perfect informal environment for collaborative research.

At the Moving Interfaces workshop, I had a lengthy discussion with Peter Smereka about the Immersed Interface Method, and how it can really be viewed as a way to discretize a delta function for the types of numerical computations that arise in moving and free boundary problems. He hadn't see that connection before, and became quite intrigued with the idea. Last spring, he sent me a pre-print of a paper expanding on these ideas and plans to submit it shortly.

Last September, I was invited to speak at the annual PNWAS meeting. I have been attending those meetings for about 10 years now, and so was happy to accept the invitation. The fact that it was in Banff only made it that much more appealing. That meeting provided me with the perfect opportunity to talk for the first time on some research I had been working on on my own, but hadn't really discussed in detail with anyone else. I had confidence in the ideas, but the preparations for talk really forced me to clarify those ideas, and put together some computational results that validated the research. I received very positive feedback on the talk and research I had done, and so left Banff confident that I should write up the research and submit it.

I strongly support the continued funding for BIRS, and only hope that more people are able to take advantage of the research possibilities there.

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Boris Solomyak, Professor, Department of Mathematics, University of Washington

I was a co-organizer of 2 BIRS workshops: Joint Dynamics, in June-July 2003, with Doug Lind, Dan Rudolph, and Klaus Schmidt, and Aperiodic Order: Dynamical Systems, Combinatorics, and Operators, in May-June 2004, with Michael Baake, David Damanik, and Ian Putnam.

I found both workshops to be extremely stimulating. Here is one concrete example: Robbie Robinson raised a question about the existence of a topologically mixing tiling dynamical system in his talk at the Joint Dynamics workshop. Together with Rick Kenyon, also a participant, we started to think about it (in fact, we had some partial results in this direction as far back as mid 1990-s, which we hadn't written down, and this question motivated us to take another look at the problem). We made some progress, and later Lorenzo Sadun, who was also a participant in both workshops, joined in this project. The question about higher-dimensional tiling systems is still open, but we obtained a nice characterization of topologically mixing substitution systems in the two-symbol case. A paper by Kenyon, Sadun, and myself has been submitted. This is just one example of a fruitful collaboration which was directly inspired by the workshop; I am sure there are more.

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David Rosenthal, St. John's University

I attended a workshop at BIRS this past April and had a wonderful time. Everyone there came away feeling that the conference was both productive and fun. The facilities were fantastic and we couldn't ask for a much better atmosphere. I hope that I have the chance to attend future meetings there.

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Laurel Fais, Research Associate, Infant Studies Centre, University of British Columbia

I participated in the workshop on ``Human Infant Speech Perception and Language Acquisition" held from March 18 to 20, 2004 at the Banff International Research Station. Actually, not only did I participate in it as a researcher involved in the project that was the topic of the meeting, but in my role as Dr. Janet Werker's Lab Coordinator, I also worked with the BIRS staff who set up the workshop for us.

Our workshop brought together primary researchers and their students, all of whom were collaborating on a wide-ranging project, from countries all over Europe and North America. Being together at BIRS allowed us to transcend the usual boundaries that had made working together at best a ponderous project: boundaries of distance, time zones, email servers, incompatible file forms and the like. We could pursue our discussions in in-depth brainstorming sessions, lecture-format talks, over a formal dinner, with coffee or wine in the lounge, in short, in any of a wide variety of venues that encouraged the unfettered interaction critically required to make a true collaboration work. And true collaboration did grow out of our workshop. Connections were made especially among students and new researchers to the project for whom face-to-face discussion was a necessary prerequisite of continued work together by email.

I would also like to comment at least briefly on the organizational aspects of the workshop. Certainly I found that the structure for setting up the workshop, inviting participants, receiving confirmations, arranging for accommodations and the like, was well-thought-out and workable. But what I appreciated the most was that once I arrived in Banff, it was no longer necessary for me to be an organizer. I could take up my role as researcher and participate fully in the talks and discussions without concern for any of the logistics of the conference. This lack of distraction made it possible for me-for all of us-to be fully participating members of what turned out to be a very productive workshop.

I heartily endorse the significant role that BIRS plays in the scientific community. My participation in the workshop there made an enormous contribution to my ability to integrate my understanding of all the various areas on which our different research teams were working and thus on my ability to represent this work accurately and effectively in the research I am doing that has grown out of that meeting.

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James McCoy, Centre for Mathematics and its Applications, Australian National University

I would like to thank you for providing a valuable service to the mathematical community. BIRS has made a difference to my research, allowing me to meet with many internationally renowned mathematicians in my area of research, people I would not otherwise have had the chance to meet. Discussions at BIRS and attendance at the talks have opened up new directions in my research and for that I am very grateful. I was also made aware of very relevant cutting edge research which has not yet appeared in print.

The facilities at BIRS were certainly of excellent standard and I have no hesitation in highly recommending it as a venue for mathematical conferences.

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Peter Webb, Department of Mathematics, University of Minnesota

The workshop on representations of algebras which I attended at Banff was particularly useful to me in that I was able to meet with an international group of experts and achieve things by face-to-face contact which would not have been possible otherwise. I went to Banff with several questions which I resolved while I was there. In one case it was a question of determining whether a certain construction is already in the literature and known to the mathematical community. In another case I was able to discuss the degree of overlap between some work of mine and work of another workshop participant. In a third case I was able to meet someone whose work I had been studying and who I could not remember meeting before (although he reminded me that we had met about 10 years ago).

These interactions have the greatest benefit to my research, and BIRS is playing a significant role in allowing them to take place.

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Jingyi Chen, Department of Mathematics, University of British Columbia

I have participated the workshop ``Perspectives in Differential Geometry" in 2003 and the workshop ``Geometric Evolution Equations" in 2004. I enjoyed both of them very much. The results reported in the workshops were most updated and some were on-going research projects. The opportunities to talk to a group of experts were highly valuable, and definitely have positive impacts in my research. From what I learn, all of the attendees of the two workshops want to come back to BIRS.

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Lyn Thomas, University of Southampton

As one of the organisers of the Consumer Credit Risk conference held in BIRS in October 2003 can I thank you for the invitation and the work you and our staff did. This is an area which has a limited academic research community spread over five continents but is of vital importance to the functioning of the economy ( Without it there would be no mass consumer credit industry). The opportunity for the researchers to get together and concentrate on the current research problems and to agree an agenda of future research was very useful in two ways. Firstly the opportunity to work closely in small groups helped develop research collaborations that would never otherwise have happened. Secondly the meeting of minds on the relative importance of unsolved research areas has given a cohesion to the community that was not previously there. All the participants I have been corresponding with subsequently agreed on how useful the conference was and the excellence of the venue for this type of interaction. In my own case the conference directly led to a paper with David Hand and Bob Oliver mapping out the future of research in this area, and the collaboration with Fabio Wendling form Brazil begun at Banff led to a grant for him to come to the UK to work together and we have produced papers on the credit risk of portfolios of retail loans which is both the first such model specifically for retail portfolios and also impinges considerably on the proposed regulations in the Basel New accord for capital adequacy, which is the major event affecting banking in the next five years.

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Raf Cluckers, Postdoctoral fellow of F.W.O.-Flanders at Ecole Normale Suprieure, Paris

My stay at BIRS has been very important and successful to:

1) broaden my contact basis with people working in model theory and real geometry;

2) present my most recent results to a specialist audience;

3) work further with coauthors on joint projects , towards publication of a research paper;

4) learn about recent progress in model theory and real geometry.

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Toms Caraballo, Professor of Mathematical Analysis, Facultad de Matematicas, Universidad de Sevilla, Spain

Indeed, I participated in a Research in Team during August 2003 for two weeks, and I am glad to say that it was an excellent experience. I had a wonderful stay, and I had the opportunity of meeting three other colleagues to work in a common project during these two weeks. We could discuss on several problems and we prepared successfully the basis for at least three papers on the field of Invariant Manifolds for Stochastic Partial Differential Equations which are still in progress due to the difficulties of the topic. Without this stay in BIRS it would have been almost impossible to obtain such results. This is why I strongly support this institution and am very grateful to them.

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Alexander Markus, Ben-Gurion University of the Negev, Israel

I have read with great satisfaction your information on the plans of the expanding of the activity of the Banff International Research Station.

I have participated in the Workshop on Linear Operators at BIRS in August 2004. The beautiful location in a national park, the computer connection in hotel room, the possibility of direct and non-formal contacts with eminent researches in my area, all of this made these three unforgettable days in the Banff Centre very nice and very useful for me.

I hope I will have additional possibilities to visit BIRS. This hope is connected, in particular, with the plans to organize at BIRS a Workshop on Numerical Ranges in 2006.

I wish you new achievements in your important activity.

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Janet Werker, FRSC, Professor and Canada Research, Chair, UBC Psychology, University of British Columbia

I welcome the opportunity to express just how positive my experience was of hosting a workshop at the Banff International Research Station this past March (2004). I am a Developmental Psychologist, interested in the effects of experience on speech perception, so you might wonder why I hosted a workshop at BIRS. In the past several years, however, it has become increasing apparent that one way in which infants develop language specific perceptual categories is via statistical learning - their minds are designed to carefully track probabilistic statistics in heard speech, allowing the tuning and retuning of native perceptual categories. This finding has reignited basic theoretical controversies in language development - do infants track just any statistical regularities they encounter, or are there tights constraints on just what can be learned, given by an innately given language acquisition device? In the first case, statistical learning is a matter of ``induction", and in the latter case statistical learning is a matter of ``selection" among already given alternative. To find a way through this morass, psychologists and cognitive scientists have turned to computational modelling - in some cases modelling the characteristics of the input, sometimes of the neural architecture supporting learning, and sometimes of both. At the BIRS workshop, we brought together psychologists, cognitive scientists, linguists, computer scientists, and engineers to discuss these issues. The quality of the discussions, and the insights provided, led to significant advances and insights both in the experiments that were designed, and in the characteristics of the computational models being developed. One focus that emerged was a need to differentiate between what we call ``shallow" learning (perceptual retuning, likely via statistical learning) from ``deep" learning (instantiation of learned regularities in actual language processing). This has already led to a number of new experiments, and is the thrust of a theoretical paper several of us are now working on.

The support provided by BIRS was invaluable to the success of the workshop. In a completely non-intrusive way, an environment was created by the BIRS staff and the BIRS facility that allowed us to concentrate purely on our work. Even as the conference organizer, I was able to assume that the rooms would be set up, the food available, projectors in place, etc., and enjoy the intellectual content of the meeting. The absolutely stunning setting is, I firmly believe, also conducive to creativity and productive intellectual exchanges. Attendees at the workshop were from Canada, the U.S. Spain, Italy, and France. All were impressed by the concept of BIRS, the facility itself, the incredibly helpful staff, and the success of the meeting. This is a gem that should be maintained.

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Maria J. Gonzalez, University of Cadiz, Spain

My name is Maria J. Gonzalez. I am extremely grateful to the

Banff International Research Station for organizing the workshop on ``Analysis and Geometric Measure Theory" in July 2003.It was an honour and a pleasure to participate in it. The

atmosphere is very appropriate to encourage discussions with the the other participants. In particular,my meeting there with J. Garnett, G. David and H. Pajot has been very helpful. Thanks to their valuable comments and explanations I have been able to better understand some topics that I have used later on in my research.

The experience was excellent and I hope it can be repeated.

Thank you.

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Serge Dubuc, Department de Mathematiques et de statistique, Universit de Montreal

I have participated in the workshop ``Applicable Harmonic Analysis" in June 2003. This meeting was an opportunity to meet Prof. Bin Han of University of Alberta. At this meeting, we planned a paper which has been completed in Fall 2003 and submitted to CAGD (Computer Aided Geometric Design) in January 2004.

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Mark Lewis, Canada Research Chair in Mathematical Biology, University of Alberta

this is a letter of strong support and appreciation for the impact that BIRS has had on mathematics in the PIMS and broader communities. From my experience it has built and strengthened interactions between researchers in new tangible ways, and this is having a major impact on research activities.

Rather than focusing on the broad impact of the workshops, FRGs and so forth, I would prefer to focus in on two examples of ``spin off" research activities that have benefited Alberta.

The first is a new collaboration with Ed McCauley (CRC in Population Ecology at Calgary). A new Alberta Ingenuity Fund Centre that McCauley codirects http://www.albertaingenuity.ca/grants evaluates water as an Alberta resource that is facing progressively greater challenges from human demands. We are now undertaking a mathematical collaboration with McCauley in the context of this large network (total annual budget approx 1.5 million). Our goal is to mathematically model the impact of stream dynamics (flow rates, nutrient levels etc.) on ecology of natural stream populations. A student/postdoc problem solving meeting at BIRS in March 04 was instrumental in getting this project off the ground, where we laid the groundwork for a long-standing collaborative thrust that involves U of Alberta and U of Calgary. We currently have a (PIMS supported) postdoc (joint with McCauley) working on the project, and have applied for additional network money for this (results pending).

More recently, we just completed a meeting on ``Biological Invasions" at BIRS (Nov 04). One species whose range is spreading into Alberta (from US and BC) is the mountain pine beetle (MPB). This devastates pine forests. In collaboration with Fangliang He (University of Alberta CRC in Biodiversity and Landscape Modeling) there is a new Alberta-based project to use mathematical models to evaluate and predict impacts of MPB. This project, recently funded by Natural Resources Canada (approx $ 500 K), is just starting (less than one month old). The recent ``Biological Invasions" meeting at BIRS brought a US expert (Jim Powell, USU) on mathematical modelling of MPB to lecture on his work over the last decade. This lecture, and subsequent afternoon discussions with Powell where we could ``test out" our modelling ideas on him, provided invaluable scientific input at the point where we are just starting this new research project. It caused us to rethink some of our approaches, and has shown us new methods we can use to improve improve the quality of the research.

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Dale Olesky, Professor, Department of Computer Science, University of Victoria

I wish to express my support for the continued funding of the Banff International Research Station. I attended a workshop there in May 2004, and it was a very stimulating research environment. It brought together researchers with common interests from across North America and more distant parts of the globe for the presentation of talks and less formal focussed discussions. While I was familiar with many of these researchers and their work, I met many new people and learned about their research ideas. Such workshops are in many ways more fruitful than conferences due to the relatively small number of attendees and the focussed nature of a workshop. One direct benefit of the workshop I attended was making contact with a graduate student from Wyoming, who very likely will work with me as a postdoctoral fellow in a few months when he completes his PhD. These workshops facilitate such interactions with current graduate students as well as established researchers.

I would like to compare the Banff International Research Station with the well established and successful Oberwolfach facility in Germany. I have attended workshops at both, and I am happy to say that the Banff International Research Station compares very favorably with the prestigious Oberwolfach site, and is a credit to the North American mathematical communities that support it. I hope that we have the vision and funding to see this continue.

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Brian O. Ma, M.Sc., Behavioural Ecology Research Group, Department of Biological Sciences, Simon Fraser University

I attended the MITACS-MSRI-PIMS Special Program on Infectious Diseases at BIRS, Banff, Alberta from June 19th to July 2, 2004. This workshop was a very rewarding experience for me. I was able connections with professors and other peers, which is always a valuable commodity. However, what was most interesting to me was the various techniques and viewpoints that came out of meeting. With speakers ranging from fellow graduate students, professors, and government scientists, the different viewpoints and aspects of infectious disease research were presented to me in a cohesive and comprehensive fashion. Many of the students that attending this workshop were from different disciplines, so each of us brought a very different skill set to the table. By working on group projects together, we were able to blend our skill sets together.

Some of the techniques that were presented in the workshop were also quite amazing, and helped me directly with my research. Specifically, we were shown four different ways of developing the basic reproductive ratio, which was something I had struggled with in my own research. Now, I have four different ways of doing it!

As a whole, the workshop provided a fun and informative experience, and I would not hesitate to attend another workshop like this in the future.

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Ted Bisztriczky, Head, Department of Mathematics and Statistics, University of Calgary

It is my pleasure to able to express my support for the renewal of the Banff International Research Station. As Head of the Department of Mathematics and Statistics at the University of Calgary,I can authoritatively state that BIRS has helped tremendously to increase research activity in the mathematical sciences at this University.The proximity of Banff to Calgary has enabled us not only to frequently participate at workshops(especially the 2-day ones) but also to take advantage of the presence of the many visiting high calibre scientists via both a BIRS Visitor Program and the occasional extensions of the workshops by an added day or two of meetings in Calgary.

As a mathematician with many international collaborators,I can also state that BIRS is viewed very favourably and appreciatively by researchers in the mathematical sciences all over the world.With the establishment of BIRS,Canada is now regarded as one of the leading countries for mathematics based research.

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Helmy S. Sherif, Professor Emeritus, Department of Physics, University of Alberta

It gives me great pleasure to send you this brief note in support of the renewal of funding for the Banff International Research Station. I have been involved in two weekend workshops held at BIRS, one in August 2003 and the second this past September. These workshops involved colleagues from the Universities of Alberta, Calgary and Lethbridge together with a number of participants from national and international institutions.

These workshops have been most helpful in bringing people from different disciplines (physics, mathematics, chemistry and computing science) together to discuss topics of research of mutual interest. I am happy to say that interdisciplinary collaborations have been enhanced due to these workshops. One evident result of these workshop is a noticeable increase in activities involving colleagues from the university of Calgary and University of Alberta, and collaboration between researchers in different department at the university of Alberta (I am sure you will learn about this from the individuals involved).

One of the common themes at these workshops was the variety of discussions involving many-body problems in various areas of physics and chemistry. In my particular case my interest is in the area of the nuclear many-body problems as it pertains to the study of nuclear structure and reactions with particular emphasis on applications to astrophysics. During these workshops I had the opportunity to discuss the work of colleagues in the United States who are involved in novel approaches to this problems. We are currently discussing the idea of holding one of the 5-day workshops at BIRS to bring together an international group of astrophysicists to forge mutual collaborations in this field. This will be a very timely course of action in view of the new astrophysics program carried out at the ISAC facility at TRIUMF.

I would like to close by expressing my gratitude to BIRS for making these encounters possible.

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Jeong-Yup Lee, Department of Mathematical Sciences, University of Alberta

I am happy to write my experience here:

My experience has been great attending BIRS conferences or visiting BIRS for ``Research in Team". I could meet many mathematicians in different areas whose work I often meet in my research. In 2004 ``Aperiodic Order, Dynamical Systems, Combinatorics, and Operators" conference, I met a group of people whose research area is a lot related with my research project. I had a question which had been in my mind for a long time. So I asked this question to one of people in that group and she could tell me the answer right away giving me a good connection to other subjects with my project.

In 2003, I had a visit to BIRS for ``Research in Team". This year we have submitted a paper of which work was initiated at that visit.

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Dong-Ho Tsai, Department of Mathematics, National Tsing Hua University, Taiwan

I attended a workshop ``Geometric Evolution Equations" held at BIRS from July 24, 2004 to July 29, 2004. This workshop is essentially the best one I have ever attended. I benefited a lot from this workshop by knowing some young researchers. I now have research collaboration with one of the young participant. This is very important to me. I think BIRS should continue its function as a research station. The facility is great also.

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Thomas Meyer, School of Computer Science and Engineering, University of New South Wales, Australia

The workshop that I attended at BIRS brought together researchers from belief revision, constraint programming, and combinatorial optimisation, with the hope of establishing common ground between the disciplines.

As a consequence, a PhD student another BIRS workshop participant, and I are currently exploring the links between belief revision and constraint programming. We expect to publish results in the next year. Also, two of the participants at the workshop have since joined the research group I am a member of. It would thus be fair to say that the workshop has had a significant effect on the direction of my research.

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Balint Virag, Canada Research Chair, University of Toronto

I find the BIRS the single most inspiring place to have a workshop, and my two stays there have been very productive. I have already accepted two invitations to future workshops.

Our paper ``Zeros of the iid Gaussian power series: a conformally invariant determinantal process" (with Y. Peres) to appear in Acta Math, has seen important progress in the summer 2003 Discrete Probability meeting in Banff. We specifically thank BIRS for this in the acknowledgements. Let me take this opportunity to thank this wonderful institution again.

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Serge Bouc, Institut de Mathematiques, CNRS-Universite Paris 7- Denis Diderot

I participated last year to the BIRS workshop ``New trends in representations of finite groups". I had the opportunity to expose my work on the Dade group of a finite group, whose structure was still unknown in general at that time. It has been indeed an open problem for more than 25 years, after original Dade's work in 1978. During my talk, I formulated two conjectures on this subject. The audience's reaction was quite motivating, and in particular Jon Alperin encouraged me to continue my efforts in proving these conjectures. It required (only?) another six months to be done, and I finally proved my two conjectures in June. It's always difficult to measure exactly the impact of contacts one may have in such conferences, but I am sure that this BIRS workshop was an essential step in my work, in that it gave me the suitable framework to at least see my future research direction, and what kind of problems had to be solved to reach my goal. For these reasons, I sincerely hope to have other similar opportunities in the future.

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Hendrik Lenstra, Mathematisch Instituut, Universiteit Leiden

This message is to express my support for BIRS. I was involved as a co-organizer in a BIRS workshop on number theory that was held in November, 2004. The workshop was roughly modeled on a series of workshops that is regularly being held in Oberwolfach, Germany. The formula of the workshop is to bring together number theorists who are active in several different areas and who share an attitude that has come to be referred to as `explicit'; this includes, but is by no means limited to, computational work, In Oberwolfach, the formula works out quite successfully, and since mathematicians from North-America have fewer opportunities to come to Oberwolfach than their colleagues from Europe, it was felt appropriate to have them share in the success by organizing a similar meeting at Banff. Now that the meeting is over, it is interesting to see the differences with Oberwolfach. The obvious and expected one was the composition of the group brought together. It was again true that they belonged to several different pars of number theory, and there were many people not commonly seen together at meetings. Less expectedly, the fields represented were not the same as those typically represented at Oberwolfach, which is provided opportunities for unexpected interactions. Several participants mentioned to me that they had made profited from these opportunities and had made new and productive contacts at Banff. I hope that it will be possible to organize similar but different meetings at Banff in the future--similar in the sense that the formula is the same, but different in the sense that the list of invitees and the precise areas covered will be reconsidered.

It may be of interest to list a few other differences with Oberwolfach. In Oberwolfach, we often organize one of more mini-series of (say) three lectures on important new developments. This may also work at Banff, though the limit of 40 participants may be subcritical. In Oberwolfach, organizers are asked to keep the early afternoon free of lectures, so that there are more opportunities for interaction. This idea would be worth considering for Banff too. The facilities at Banff are excellent, except for the lecture room (which is a bit cramped) and, naturally, the library. The management is efficient and less heavy than at Oberwolfach. In summary, BIRS should be cherished and deserves a long life, all for the benefit of mathematics. I do wish you all success with renewing your grant.

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Bill Jackson, School of Mathematical Sciences, Queen Mary, University of London

I attended the Banff Workshop on the Flexibility of Protein Molecules in July this year. I can honestly say it was one of the most stimulating meetings I have been to in my 25+ years as an academic. Certainly I have never been to a meeting which provoked such heated discussions. Attending the workshop motivated me to concentrate my research efforts into attacking the Tay-Whitely Conjecture on the rigidity of molecular frameworks. (Whitely was one of the workshop organisers and Tay attended the workshop.) I am taking leave of absence from my university from January to April 2005 in order to visit T Jordan (another participant at the workshop). Our aim is to work on the above mentioned conjecture and also on the more general problem of determining when a framework is rigid in 3D.

Another spin off from the workshop is a paper I am currently writing in collaboration with Brigitte and Herman Servitious which investigates the global rigidity of certain families of graphs in 2D. This joint research was instigated during the workshop. We intend to submit our paper for publication in the near future.

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Justin Sawon, Department of Mathematics, SUNY at Stony Brook

I participated in the November 2003 workshop ``Interaction of Gromov-Witten and finite-type invariants", and have recently finished a survey article entitled ``Perturbative expansion of Chern-Simons theory" for the workshop proceedings. The highlight of the workshop for me were the lectures by Marcos Marino: it was great that we could invite a physicist to give a series of lectures about a very interesting, though mathematically underdeveloped topic.

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James Wadsley, McMaster University

The BIRS facility was a superb place for a scientific meeting. The accommodation and other facilities for recreation, dining and other services were all excellent, and significantly more pleasant than what would typically be available at a regular hotel.

The scientific facilities including meeting rooms, talk presentation equipment and internet were all fantastic. It was very easy to use with no bottle necks or problems. Unlike most conferences, we were easily able to remotely look at work, reference material and even simulation results during the conference via internet. This is a rare and valuable capability. The set-up was very conducive to a good workshop. The site (with its beautiful views) and facilities attracted good people from as far away as Europe and made our meeting a great success.

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Paul Tod, Mathematical Institute, Oxford University

I am writing in reply to your request for feedback on my experience as one of the participants at a workshop, specifically 04w5006 Conformal Geometry, this summer.

I had a very constructive time at the workshop. Conversations with Michael Eastwood and Rod Gover gave significant help in two directions with the problem of conformal gauge symmetries described in my talk. This is work I am actively engaged in with a student. Conversations with Claude LeBrun and Gideon Maschler cast light on a problem in the study of Einstein manifolds with torus symmetry which I was involved in with another student, but persuaded me that it wasn't going to work! I also had useful interactions with Robin Graham, Lionel Mason, George Sparling and Maciek Dunajski.

The style of life and organisation and layout of the Centre all contribute to making it a good place to work. The administration is helpful, flexible and good-humoured. The Centre is well-run and a definite asset to the mathematical community. I wish it a long life.

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Ron Graham, University of California-San Diego

I'm sorry I wasn't able to attend the recent PIMS Board meeting in Vancouver. I actually arrived in Vancouver the day before, but a serious cold (and laryngitis) struck, so I thought I would spare exposing the other committees to any of the accompanying viruses! We also overlapped for a day at BIRS last week but I missed bumping into you there as well!

It is clear that BIRS has been (and is continuing to be) a very positive force in the world on mathematics. I'm sure this will put a lot of pressure on Oberwolfach!

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Karin Erdmann, Mathematical Institute, University of Oxford

During the meeting (Interactions of finite-dimensional algebras...) highlights for me were the lectures by Ginzburg (for general background), and the work by Schroer/Leclerc (related to Calabi-Yau dimension for self-injective algebras). Apart from this, discussions during the meeting helped me to finish a paper (which has now been submitted and provisionally accepted).

Meetings of this kind are extremely important and I hope very much that BIRS will continue

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John Steel, Department of Mathematics, University of California-Berkeley

I attended the set theory workshop in early May 2004, organized by Matt Foreman. It was an excellent meeting; I met some younger people I hadn't met before, learned parts of some work by Hugh Woodin which I am trying to build on now, and even proved a little theorem during the conference. The beautiful setting, and the quiet, relaxed atmosphere at BIRS contributed a lot to this success. The staff was very friendly and helpful, and their efficiency made it easier to focus exclusively on mathematics.

It's a great place to have a math conference - I'd love to return!

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Hans Weinberger, Department of Mathematics, University of Minnesota

I attended the workshop on Mathematical Models for Biological Invasions from November 27 to December 3, 2004. While it is clearly too soon to discuss its long-term effect on my work, I found it an excellent occasion to make the acquaintance of a number of bright ecologists. It was very useful to learn what methods they use to acquire and treat their data, and to hear what they would like to know. In addition, I was able to discuss some mathematical problems with other mathematicians with similar interests, including some young people whom I had not met before. I got a number of ideas for future work, which I hope to pursue shortly.

I should mention that BIRS is an ideal setting for such a conference. I found the close contact with a small group of people and a schedule which left much time for informal discussion to be extremely useful. There was plenty of space for working with small groups, and the meals were not only delicious, but provided a good setting for getting to know people.

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Anant Godbole, Department of Mathematics, East Tennessee State University

The BIRS workshop on DeBruijn Cycles and Gray Codes was timely, appropriate and high-level. It was immensely useful for me in seeing the broader context of the research that I was doing. The local organization was far better than that at other Math Institutes and a special note needs to be made of Andrea Lundquist's quiet efficiency. The Oberwolfach setting was again better than at other Math Institutes that I have been to. Renewal of funding for BIRS is, to my mind, a no-brainer, given the topics of the workshops and the extremely high standards that have been set from the very beginning.

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Andrei Mikhailov, California Institute of Technology

I participated in the String Field theory camp, organized by Gordon Semenoff and Mark Van Raamsdonk. I was very much impressed by the center, the fabulous location and excellent conditions for work. At that time I was thinking about some aspects of the classical string dynamics in AdS space. The results of that work were reported in my paper hep-th/0409040 (I expressed my gratitude to the organizers in the Acknowledgement section of that paper).

Thanks a lot for the excellent time I spent at BIRS!

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Lawrence Ein, University of Illinois at Chicago

I was a participant of a workshop on commutative algebra and singularities theory at the Banff International Research Station this Fall. I enjoy very much the workshop. It provides me, a complex algebraic geometer, a very nice opportunity to meet some of top commutative algebraists in the world. In particular I found the discussions with some of the Japanese colleagues working on tight closure theory are particularly useful for me. The similarity between the results obtained using analytic methods and pure algebraic methods using Frobenius morphisms is just simply fascinating. I appreciate very much the opportunities provided by the workshop at BIRS to interact with these colleagues.

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Stefan Friedl, Rice University

I stayed at BIRS for a 5-day workshop with the title ``Knots and their manifold stories". This stay turned out to be very productive, not only did I get introduced to a number of new research areas but it also started a collaboration with a Korean knot theorist which would not have started otherwise. I hope that BIRS will be funded in the future, it is of major importance to the mathematical community.

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Craig A. Tracy, Department of Mathematics, University of California-Davis

I found my stay at BIRS most beneficial. It was the first ``all combinatorics'' meeting I have ever attended and it broadened my perspective. It also allowed me to meet many people who previously I had just known from their research. All and all a very pleasant stay.

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Kenichiro Kimura, Institute of Mathematics, University of Tsukuba

I participated in the workshop

''Calabi-Yau varieties and Mirror symmetry'', December 2003.

Before this I had never been in contact with physicists and had never been given motivation of research from them. In this workshop I could learn what kind of problems are discussed and studied at the front of this fascinating field and it was extremely useful.

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Alan Hopenwasser, Department of Mathematics, University of Alabama

I respond with pleasure to your request for information about my Banff International Research Station experience in December 2003. The one word answer is: superb!

The facilities at BIRS are excellent, with first rate amenities. Everything about the workshop was conducive to maximizing the mathematical benefits of the meeting. I much prefer workshops of the size held at BIRS to larger meetings, primarily because, as at BIRS last year, they facilitate substantial contact with other specialists in my area (operator algebras).

In the specific instance of the workshop which I attended, about half the lectures touched on one relatively new topic (quiver algebras and free semigroup algebras). This afforded me the opportunity to get a good idea about the current research in this area. In principle, I could do the same by reading all the preprints in the area at home - but this would never happen due to other demands on time. The BIRS workshops provide a much more efficient way to keep up with current research.

At the time of the workshop I was in the midst of preparing a paper (``Subalgebras of C*-algebras") with two coauthors, both of whom work at locations distant from my home university. One of the coauthors also attended the workshop; the relaxed pace of the workshop gave us ample opportunity to make significant progress in the preparation of the paper.

To summarize: the workshop which I attended at the Banff International Research Station was amongst the best I have ever attended. I certainly hope that I will visit BIRS again in the near future.

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Maria Del Mar Gonzalez, Department of Mathematics, Princeton University

I participated in the BIRS workshop: Monge-Ampere type equations and applications, in August 2003. I was then a graduate student. This workshop in Banff had a great influence in my mathematical life since I gave there my first seminar. I had the opportunity to speak to a wide audience, interested in areas a little bit different than mine, but still related and with a lot of ideas to share.

I had some interesting conversations with prof. Guan and prof. Wang, whose work is related to my paper 'Singular sets of a class of locally conformally flat manifolds', to appear in Duke Journals.

I also met Prof. Martinez-Maure, from France. This was very useful since I was going to start a postdoc there shortly after but I didn't know many people in Paris yet.

And finally, but not less important, the economic support from the organizers gave me this opportunity since, as a graduate student, I did not have much chance to travel. Now I am going to start a position in Austin, TX, but still, I would be happy to participate in future BIRS programs.

Good job!!

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Lei Feng, Ph.D. Student, University of Toronto

I attended the Banff DES Workshop in May 2004. It was my first time to attend any academic conference or workshop in my Ph.D. study. I felt excited to meet those professors and follow students whose names had been very familiar to me through their publications. I could clarify some puzzles about their work in person and discuss with them on any possible topics. In the workshop, I noticed that some researchers' works might be helpful to me, but I had never thought to check out those kinds of publications. The wonderful effect of that workshop is to organize people with similar topics but different perspectives together. The discussion was fun and inspiring.

I presented some premature ideas in the workshop. Receiving positive feedback, I felt more confident on my work. Now the idea becomes polished. I am testing the idea on various benchmarks and hoping to write a good paper about it.

I hope I have chances to return Banff in the future. There are still a lot of beautiful scenes I have not visited.

Thank you for your organization!

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Yuval Peres, Professor, Departments of Statistics and Mathematics, University of California-Berkeley

I attended (and helped organize) one two-week meeting at BIRS, and have already accepted two invitations for additional visits.

The two weeks I spent at BIRS have motivated much of my work in the 18 months since I visited there. In particular substantial progress was achieved there in work with Balint Virag (Toronto) on ``zeros of the IID Gaussian power series" (paper to appear in the leading journal Acta Math) and in work with Dimitris Achlioptas (Microsoft Research): resulting paper appeared in Journal of the AMS, as well as in ongoing collaborations with Alexander Holroyd (UBC).

Until 2003, the leading venues for week long meetings were, perhaps, Oberwolfach (Germany), MSRI (California) and the Newton institute (England). In a very short time BIRS has joined their rank, and (having visited all of these institutes) I would say that BIRS is now the most inspiring and well equipped venue for mathematical meetings I am aware of.

The existence of BIRS is a valuable addition to the mathematical landscape in North America, and in particular raises awareness of the vigor and stature of Canadian mathematics and encourages more effective collaboration between Canadian mathematicians and Mathematicians based elsewhere.

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Rolf Schneider, University of Freiburg, Germany

I am glad to hear about the proposal being put together for a renewal of the Banff International Research Station, and for an expansion of its operation. I have been there this year for the first time, after more than 25 visits to the Mathematisches Forschungsinstitut Oberwolfach. My impression was that BIRS is an equivalent to Oberwolfach on the North American continent V among mathematicians this says enough to praise it. These opportunities to meet new people and to exchange information about latest results in the own and neighbouring fields are of the highest value for the progress of our science.

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Jian Pei, School of Computing Science, Simon Fraser University

As a participant to the BIRS data mining workshop, the workshop helped me a lot. It was the first academic meeting I took part in after I moved to Simon Fraser University. One unique feature I like very much is the joint effort from both academia and industry. It provides me important information about the industrial applications. The connections to industrial people are equally important.

I fully support the growth of BIRS, and believe that it would strongly help many junior faculty members like me in Canadian universities.

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Dimitris Achlioptas, Microsoft

I participated in http://www.pims.math.ca/birs/wor
kshops/2003/03frg003/participants.html

During my stay there, Professor Yuval Peres and I had the opportunity to collaborate on (what we thought were) the final stages of our article http://www.pims.math.ca/birs/workshops/2003/
03frg003/participants.html

It turned out that while working on the final version to submit, we reopened an open question in our work and completely settled it! This is now a significant part of the article. I believe that the environment and pace at BIRS was instrumental in allowing us to revisit the question.

Also, I had the opportunity to meet Balint Virag for the first time, with whom I had a number of very interesting research discussions.

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Maarten van Emden, Department of Computer Science, University of Victoria

I attended the workshop on Belief revision, constraint programming, and combinatorial optimization May 24-29, 2003, organized by R. Goebel.

This workshop was an enormous boost to my research. I had been specializing in constraint programming, considering it as an offshoot of logic programming. I was only vaguely aware of its connections with AI and with OR. Not only was it an eye-opener to learn about such connections, but it came with prominent researchers in these other areas that I found myself sitting next to during the talks or during the lunches and the dinners.

BIRS is created to be the ideal research environment. Part of it due to whoever created the mountains and the views. The rest is due to the amenities. That includes the ideal connection to the internet, the campus-like atmosphere, the pleasant walk to a nice town, and the great food. The list is too long to include here. But special mention should be made of the excellent network and computing facilities. A good scientific conversation nowadays requires frequent references to things on WWW. BIRS is near-ideal for this: I had a terminal with a Unix account in my room as well as an instant connection for my laptop. I would not be surprised to find wireless access on my next visit.

This fantastic environment works directly, in the obvious way. I should also mention that stars like Pulleyblank and Hooker would probably not have come if the workshop had not been in Banff. I think this is an important effect.

But equally important contacts for me are in BC. Science administrators might think that I don't need help in getting to meet these. The reality is different. My meetings with Hare, Mackworth, and Havens were long overdue. All in all, I had valuable interactions with at least 50other meeting in recent years has come close to that percentage.

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Volker Gebhardt, School of Quantitative Methods and Mathematical Sciences, University of Western Sydney

I participated in the workshop ``Braid Groups and Applications" in October and this was indeed extremely beneficial for my research. I am still in the early stage of my academic career and meeting colleagues and establishing new contacts and collaborations hence is very important for me. The workshop at BIRS proved to be valuable and successful in this respect.

I started a collaboration with Prof. Joan Birman and Dr Juan Gonzalez-Meneses at this meeting. It was the first time I met them; we had been working separately on the conjugacy problem in braid groups and decided at Banff to join forces. We cannot report papers yet (the workshop was only 7 weeks ago), but we have made some progress and are very optimistic.

I was invited to visits to New York and Seville (Spain) during the workshop. The new collaboration initiated at BIRS also lead to a grant application (travel funds). The outcome of this application is still open.

I was also asked during the workshop to write a survey article (``Conjugacy search in braid groups" under review for publication in Applicable Algebra in Engineering, Communication and Computing). I am not sure whether this would have happened otherwise, so I definitely count this towards the benefits of attending the workshop and meeting colleagues working in my area.

I would like to take the opportunity to thank you and the very supportive and friendly staff at BIRS and I hope you can keep up or even expand the good work!

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Robert Lipshitz, Mathematics Department, Stanford University

I am a graduate student at Stanford University, and participated in the BIRS / MSRI ``hot topics" workshop in 2003 on ``Floer homology for 3-manifolds." My participation was, for me, quite productive. Most specifically, in conversations with several of the other participants (P. Melvin, J. Rasmussen, and Z. Szabo) I became aware of a conjectural formula for the Maslov index in Heegaard Floer homology, which I was able to prove with the techniques I had been developing. The formula was also one of the last steps in a project I was working on; knowing what was expected to be true made it significantly easier to proceed.

More vaguely, the talks during the workshop made me more familiar with work related to mine. This helped suggest directions likely to yield interesting results later. It also allows me to avoid duplicating work currently being undertaken by other people.

The environment at BIRS was ideal for discussing mathematics. The staff took care of all non-mathematical details so that we could focus on doing mathematics. Being able to walk in the mountains while discussing our work created a relaxed but focused atmosphere, leading to a pleasant and productive trip.

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Jan Slovak, Vice-rector for Strategy and Development, Masaryk University in Brno, Czech Republic

I am very pleased to hear about your plans concerning BIRS. I had the pleasure to participate the 5-day workshop 04w5006 Conformal Geometry, held in the period Jul 31 through Aug 05 this year.

I must say the facilities, the working atmosphere, the Nature around had not been matched by my earlier experiences with similar workshops worldwide. Moreover, the organizers put together various groups of researchers seemingly staying wide apart, but with matching interests or goals. Thus I had learned a lot and I also closed new partnerships for my further research. In particular, my interest in the so called Q-curvatures had been initiated right there.

I hope very much to be able to come back to BIRS at another occasion.

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Kurt Jetter, Professor of Mathematics, Universitaet Hohenheim, Germany

I want to take the opportunity to thank you once more that you have given me the chance to participate in a workshop at your institute at Banff. This is a beautiful setup giving researchers the possibility to combine their scientific efforts with gorgeous experiences from nature.

The workshop on 'Applicable Harmonic Analysis' in June 2003 has had a big impact on my own work. Not only that I could meet some old friends and dear colleagues: It was, in particular, a very good opportunity to meet some strong young people from North America working in this area. Concerning the subject, this workshop has confirmed my decision to go more into the new and challenging subject of applications of frames to problems in signal processing.

So thank you again. And I do hope that I will have the chance to meet there in the future,

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Jan Wiegerinck, Department of Mathematics, University of Amsterdam

I am happy to explain how useful participating in the workshop pluripotential theory has been for my research. It boosted an E-mail cooperation with Poletsky, who was also participating.

Moreover, meeting Ransford, whom I had not expected to see, because he works a little outside my field, helped me to answer a nagging question (in fact he solved it!)

The workshop was well organized. The format, bringing together experts from within a field with some very good people who can make connections to other parts of mathematics, is interesting, and as I explained, turned out very well for me.

The conditions created by PIMS at BIRS are excellent!

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Rachel Kuske, Canadian Research Chair, II, Department of Mathematics, University of British Columbia

This letter is in support of the funding renewal for BIRS. I also hope that its operations will expand.

I have been involved in a number of meetings at BIRS, all of which have been very productive and enjoyable.

My first visit to BIRS was as coorganizer of the PIMS/IMA Graduate Students Mathematical Modeling Workshop in May, 2003. BIRS was a great place for hosting this workshop, with an environment that supported the groups working in teams. We received a lot of positive feedback from both the students and mentors.

The second time I was at BIRS for a Workshop on Localized Patterns, in August, 2003. Again the environment at BIRS made it a perfect place to interact with experts in the workshop.

In summer 2004 I had the opportunity to organize a 2-week Research in Teams on Stochastic Differential Delay Equations. The BIRS RIT provided a much needed opportunity to meet with specialists in this area over a longer period, bringing together a variety of different viewpoints. There are a number of ongoing projects as a result of this RIT.

In Summer 2005 we will hold a two day workshop at BIRS, which is the second Connecting Women in Mathematics across Canada workshop. We look forward to holding this at BIRS, as we feel it has the a great setting for a small meeting such as this.

I look forward to seeing BIRS continue in its vital role in the support of research in the mathematical sciences.

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Otmar Scherzer, Institute of Computer Science, University of Innsbruck

I have participate at two of the meetings at BIRS. The meetings always have been very stimulating. The location is extremely exciting. There is a relaxed atmosphere where you can do significant exchange of research ideas w