Participant Testimonials
I used the workshop to present work by my PhD student Pornrat Ruengrot. The work is of a speculative nature, and the BIRS workshop was an ideal opportunity to seek ideas from an audience highly specialized in this area as well as to seek reassurance that we are on the right track. As a result I was told about two pieces of work, one unpublished, which are very relevant to his research and resolve one problem that we had been working on. The workshop also allowed me time to talk in depth with some experts on the representation theory of finite groups of Lie type, which has been very valuable in an ongoing research problem on blocks with elementary abelian defect groups of order nine. It also allowed me time to work with a Japanese collaborator in the same research. Overall, the workshop brought me into contact with many of the key players in my field of research, all concentrating on a specific set of problems. I feel that I am fully caught up now with current developments and have a clear idea of what people are working on right now.
The conference gave me the opportunity to have two short, good discussions: one with Michel Broue about the ongoing project by him, Bhama Srinivasan, and myself; the other with Britta Spaeth about the current state of a question on Harish-Chandra induction and Galois actions which she and I considered two years ago. The intimate, relaxed setting of Banff gave a directness and immediacy to mathematical discussions. The range of talks was excellent, going from the intricate, difficult nailing-down of individual cases needed for current inductive proofs to bold, engaging, new examinations of basic questions. We all went home with much to think about.
The workshop was extremely informative and inspiring. In particular I had the chance to talk to two of my colleagues about a joint research project. Such a workshop is a perfect opportunity to advance pending projects. Meeting your collaborators at an inspiring place and having enough time for discussions is extremely helpful.
Last week I stayed a week in Banff BIRS to attend Global/local conjectures in representation theory of finite groups. First of all I really thank the BIRS for such a wonderful hospitality, and also for such a nice opportunity to do wonderful mathematics. More precisely, I experienced the following: (1) I could communicate a lot with Charles Eaton (Manchester, UK), with whom I talked about one of the most important and interesting conjectures/problems in representation theory of finite groups. It was on Alperin's weight conjecture and also Broue's abelian defect group conjecture for a particular blocks with elementary abelian of order p squared. By the way, Broue attened this meeting in BIRS, and Alperin did not but his name was on the list at the beginning. Actually, because of this meeting in BIRS, Eaton and me have started our collaboration on the subject. (2) I could talk a lot with Britta Spaeth (Aachen, Germany) on our mathematics. Especially she and me discussed much (so-called) Dade-Glauberman-Nagao correspondence, which is also one of the most important problems in representation theory of finite groups. Dade was by the way one of the participants in this meeting in BIRS. The discussion with her was so efficient and useful for my research. (3) I spoke with Gerhard Hiss (Aachen, Germany) a lot. We talked on Donovan's conjecture for a particular p-group say elementary abelian of order p squared. We talked also on the classification problem of blocks of finite groups up to Morita equivalence under a mild hypothesis. (4) I discussed block structure of finite groups of Lie type, with Michel Broue, Paul Fong and Bhama Srinivasan. It was also quite important and useful for my research. Finally, I really would like to thank the BIRS for the meeting. For me it was the second time to be there (the first time was in October 2003, when Alperin, Broue, and Cliff organized a meeting in BIRS). I really appreciate it. I wish this kind of program would keep on going, and hopefully I would like to attend it again in BIRS. Thanks a lot again.
Yes, I have learned about the "basic set" conjecture directly from the people involved in that, and I am already thinking on a way to reduce it to simple groups. If I succeed, this of course will be a collaboration with several of the simple group people that attended the conference. I helped Britta Spath to find a missing piece that she had in a key paper that she is writing now (and on which she spoke in Banff). I met Evseev and was able to think about his conjecture more properly. One of the most important things at the workshop was an informal meeting that several had, in which the map of the road to finish some of the conjectures was drawn.
The impact on my research is quite large. I learned from Shigeo about a recent preprint "about a minimal counterexample for the Alperin-McKay conjecture" from Masafumi Murai (related to my own project, some of my minor results are also proven there, but with completely different very inspiring methods.) Gabriel Navarro proved for me a congruence, by which I can adapt the reduction theorem for the Alperin-McKay conjecture to the Isaacs-Navarro refinement. It enables me to strengthen my results. I discussed some stuff with my former colleague for our ongoing project, where we want to prove that PSL_n(q) satisfies the inductive McKay condition, and about possibilities to generalize elder results towards the inductive Alperin-McKay conjecture. Also with some other participants I had some nice interesting conversations, which were very inspiring and will be helpful for my further research.
In my view this was a very successful workshop. The participants were a judicious mix of senior, mid-level and junior researchers. It was also focused on a topic familiar to all the participants. As a result I was able to learn from every lecture and have discussions with most of the participants. My current research, which I presented at the workshop, is connected with the work of three of the participants. Thus discussions with these participants led to new insights and ideas for my continuing research. It was also interesting to meet some of the junior participants for the first time and to learn what they are working on. In turn some of them asked for information regarding my talk, such as copies of my slides.
The workshop's scientific program was focused and well-organized. All the talks were interesting (in fact it was the opinion of several participants including non-speakers that I talked to that all the talks at the workshop were uniformly of high quality!) Several important results were announced during the workshop (my co-organizers and I will write about them in details in the report), some by young participants. Following these new developments, we had informal discussions to coordinate the efforts of researchers from several countries to work on a set of fundamental conjectures in the field. I also had fruitful discussions with my collaborators (including Gabriel Navarro and Gunter Malle) on ongoing joint research projects.
