Participant Testimonials
BIRS is a wonderful place to work with people that have common interests. The atmosphere, the faciities, and the great surrounding are very inspiring. With the workshop I had the opportunity to meet people whose work I knew very well and discussed several ideas.
I have found the workshop "Crossing Numbers Turn Useful" very stimulating. We had plenty of opportunities to work together on various problems, which we certainly used. In particular, in addition to continue already existing projects/collaborations I have started a collaboration on new project that was motivated by crossing numbers but which is a different area. I feel that we have made tremendous progress and hope to be able to return to Banff for similar programs.
The workshop was very nice. The small number of participants (20) gave it a friendly atmosphere. We have attacked several problems outlined at the problem sessions, and at the end of the workshop some serious success has been reported. Personally, I am already preparing a manuscript with Zdenek Dvorak about computability of the average crossing number, a problem asked at the meeting by B. Richter and G. Salazar. I also took opportunity to work with Dvorak and Hlineny on our long time involvement towards describing structure of crossing critical graphs. Nice partial success was achieved.
This has been really the perfect workshop. It has achieved the perfect balance in putting together a group with different backgrounds but definitely with common interests. As a result, the work these days has been really enriching, opening new approaches to important classical problems and new insights to the relation between different, but neighboring fields.
BIRS provided an excellent opportunity for communication and collaboration within the crossing number community through this workshop. The facilities are excellent and the location is beautiful. Thank you for supporting our workshop! With Balogh and Czabarka we checked that certain type of arguments cannot prove the Albertson Conjecture - but still proved something positive. We also formulated a new conjecture: the crossing number of the complete on n vertices is a concave up function. The truth of this conjecture would effect the truth of the Albertson Conjecture. As the these crossing numbers of complete graphs are asymptotic to (an unknown) constant times n^4, this conjecture is true unless the crossing number show a very erratic behaviour, which is certainly not present for the first few known values. With Bokal and Czabarka, we collaborate on a topic on how to optimize lower bounds for crossing numbers that can be bigger on a subgraph than on the whole graph. Although we started this project earlier, meeting in person moved the project ahead.
