Participant Testimonials
The meeting did achieve its primary goal to foster interaction among topologists, geometers and combinatorialists all working in the area toric topology and geometry. I think it's fair to say that the meeting represented a significant turning point in overcoming language barriers among the three disciplines. Our report will reflect the fact that speakers all made a determined effort to be understood across the cultural divide. Indeed, it was a common sight to see mathematicians in related but different fields engaged in spirited conversations. For me personally, the meeting provided an extended opportunity to meet with my collaborators, Nigel Ray, Dietrich Notbohm and Matthias Franz. We spent two long evenings in the seminar rooms working on our project classifying weighted projective spaces. The workshop made it possible for the four of us to meet together for the first time since the project started. I managed also to have useful discussions with various participants about a paper Fred, Sam, Martin Bendersky and I completed just before the meeting on the topic of fan reduction for toric varieties. Various new questions about a construction used in that work arose and were resolved at the meeting. Our new project concerning the identification of certain moment-angle complexes as wedges of spheres, rationally, benefited from conversations we had at the meeting. Another construction on simplicial complexes, which allows the iteration of moment-angle complexes and polyhedral products, had its genesis at the workshop. The construction warrants further investigation and I have written already to fellow participant Carl Lee about the combinatorial aspects of the construction. We have received many enthusiastic and favourable comments from participants. Critical to the smooth running of the workshop was the extremely competent support we received from your excellent staff including Wynne, Brenda and Brent.
I found the conference to be mathematically compelling, and stimulating for the following reasons. (1) Generally, speakers in different areas made solid efforts to communicate how their topics informed on the main areas of the conference. I will take the liberty of pointing out several new structures which I learned about at this conference. (2) S. Lopez de Medrano and A. Verjovsky explained privately how spaces which we now call generalized moment-angle complexes (macs) give equivalence classes of natural dynamical sysems for which a theorem of Camacho, Kuiper, and Palis gave a complete topological invariant distinguishing these dynamical systems. Just this short communication raises several new, and compelling questions for me. S. Lopez de Medrano touched on this point in passing during a beautiful expository lecture, but the setting for the conference provided a wonderful opportunity to learn more.. (3) Mike Davis developed features of local systems in the group algebra of certain discrete groups given by the fundamental group of certain moment-angle complexes. After talking with Mike, the question of whether one can develop 'parametrized macs' arising from representations of their fundamental group looks quite interesting. (4) These 'accidental' contacts have had an impact on my own research which would have not occurred had this conference not been held. I for one found the conference and contact with the participants to be very stimulating, and informative. That BIRS is willing to support such activities is a wonderful contribution to the subject !
Mathematics, University of Rochester
The meeting gave the participants a unique opportunity to meet and discuss with colleagues problems that were being studied in several different areas which included Commutative algebra, algebraic geometry, Combinatorics, dynamical systems, Mathematical Physics, symplectic topology, and algebraic and differential topology.This opportunity will undoubtedly was ideal to start collaborations, I am very optimistic that this will happen soon. The facilities were superb and I want to commend Brenda for her work.
This was a very successful workshop for me ... the workshop had a fantastic impact on my current research by promoting my new result and by giving me a fresh insight and new directions to my future research. I definitely established new contact with few researchers which I wanted to meet in last several years. The workshop just confirmed that Toric Topology is a hot research area with active and successful future.
School of Mathematics, University of Manchester
1) I had the opportunity to interact with Eduardo Gonzalez, who is working on orbifold toric varieties from the point of view of computations in quantum cohomology. This conversation substantially impacts a current project I have on orbifold toric varieties. 2) I also found useful several conversations with Alejandro Adem concerning twisted orbifold Chen-Ruan cohomology, a topic relevant for my joint work with Derek Krepski, another BIRS workshop participant. 3) My postdoc Derek Krepski (mentioned above) was able to meet a large number of researchers working in this area. This will be important when he goes on the job market next academic year (fall 2011). 4) I had several useful conversations with Susan Tolman and Tom Braden which keeps me abreast of developments in their respective research areas.
I experienced fruitful and stimulating discussions with mathematicians from many countries. During the conference, I met many friends and learned their idea in their fields. I found some problem which will be extended to write a paper. In usual conferences, we have chance to communicate only in the lecture hall. But this time, I had chance to discuss mathematics even when we eat meals ... I like the lounge in the Corbett Hall. Every night, I learned many mathematics from people there.
Mathematics, University of the Ryukyus
During the workshop I had the opportunity to meet some of the top researchers in my field of research or closely related fields. I also had the chance to meet some of my collaborators. This had very good impact on my current research. Definitely it motivated some new ideas, research and possibility for some future collaborations and papers.
