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BIRS 2003 Scientific Report BIRSBIRS 20032003 AANNUAL RREPORT Banff International Research Station for Mathematical Innovation and Discovery Foreword What a great start for the Banff International Research Station and what an honour it is for me to report to the world about its very first year. BIRS, this unique bi-national partnership between Canada and the US in mathematical research, came into fruition as a result of extensive work and commitment from a great number of dedicated people on both sides of the border. To all of them, and especially to the first BIRS Scientific Director, Robert V. Moody, we dedicate this very first annual report which confirms what had been envisioned all along: BIRS is already a tremendous international resource that has created new opportunities for mathematical researchers while optimizing the use of these resources to support collaborative scientific inquiries in North America and the world. BIRS is already the ultimate centre for scientific interaction: a place where promising ideas develop, where lines of thought converge even when coming from different backgrounds (pure, applied, computational or conceptual) or different motivations (curiosity driven or industrially motivated), where people interested in similar problems unite their potentials and join their efforts in order to work on common research projects. As one can see in this report, key to the meteoric success of BIRS in its very first year, were the breadth, quality and originality of its scientific activities. BIRS interdisciplinary programmes frequently included Fields Medalists, Nevannlina prize winners and Nobel laureates, but the programmes also provided excellent opportunities for training young mathematical scientists as they gained access through BIRS to the world’s leading experts in their fields of interest. BIRS first year witnessed several scientific breakthroughs, but how one can describe the work of 2000 researchers from over 400 institutions in 49 countries participating in 68 programmes spanning every aspect of the mathematical sciences and their applications? Noteworthy among others was the announcement by Vladimir Voevodsky of his proof of the Bloch-Kato conjecture at the workshop on Quadratic forms, algebraic groups, and Galois cohomology held in October 4-9, 2003. This was an important result, which extends his own work on Milnor’s conjecture for which he won a Fields medal in 2002. The Institute of Advanced Study in Princeton is now running a yearlong program devoted to the Bloch-Kato conjecture. BIRS in 2003 was also the home of a dazzling array of scientific activities: besides the “Oberwolfach-style’’ 5-day workshops and “Research-in-Teams“ programmes, BIRS hosted Focused Research Groups, national Chairs meetings, gatherings for Women in Mathematics, summer schools in emerging areas, modelling camps for graduate students, training Camps for national Math Olympiads teams, industrial fora, and “ateliers” in scientific writing. So many opportunities for so many people … let’s all wish it a long life! Nassif Ghoussoub BIRS Scientific Director 1 contents 5-day Workshops ..................................................................................................................... 3 2-day Workshops .................................................................................................................... 47 Summer Schools, Research in Teams, Focused Research Groups ....................................... 55 2 BanffBanff InternationalInternational ResearchResearch StationStation 20032003 5-day Workshops 3 4 Recent Developments in String Theory March 15–20, 2003 Organizers: Jim Bryan (University of British Columbia) Moshe Rozali (University of British Columbia) Steve Giddings (UC-Santa Barbara) Gordon Semenoff (University of British Columbia) Mikhail Kapranov (University of Toronto) Mark Van Raamsdonk (University of British Columbia) Andreas Karch (University of Washington) K. Viswanathan (Simon Fraser University) Amanda Peet (University of Toronto) At present, there are a number of important facets of string theory in which physics is related to deeper mathematics. These include the relationship between Yang-Mills theory and gravity (the AdS/CFT correspondence), work on matrix models and supersymmetric gauge theories, mirror symmetry and classification of string compactifications through techniques such as the derived category, topological string theory, and string compactifications with fluxes, with their relationship to cosmology. The workshop provided an opportunity to survey some developments on these subjects, and to catalyze further work in these directions. The workshop provided a first-class atmosphere for interaction between speakers and for research, and was well received. Work performed at the conference included Douglas finishing the paper “The statistics of string/M theory vacua,” JHEP 0305 (2003) 046, which discusses a new approach to the study of superstring compactification. For details, please refer to the report online: http://www.pims.math.ca/birs/workshops/2003/03w5024/report03w5024.pdf Participants: Aspinwall, Paul (Duke University) Minwalla, Shiraz (Harvard University) Brecher, Dominic (University of British Columbia) Morrison, Dave (Duke University) Bryan, Jim (University of British Columbia) Myers, Robert (Perimeter Institute) Donagi, Ron (University of Pennsylvania) Ooguri, Hirosi (California Institute of Technology) Douglas, Michael (Rutgers University) Page, David (University of Toronto) Furuuchi, Kazuyuki (University of British Columbia) Peet, Amanda (University of Toronto) Getzler, E. (Northwestern University) Randall, Lisa (Harvard University) Giddings, Steve (UC-Santa Barbara) Rozali, Moshe (University of British Columbia) Gukov, Sergei (Harvard University) Schleich, Kristin (University of British Columbia) Hellerman, Simeon (Stanford University) Schreiber, Ehud (University of British Columbia) Hori, Kentaro (University of Toronto) Semenoff, Gordon (University of British Columbia) Itzhaki, Sunny (Princeton University) Sethi, Savdeep (University of Chicago) Kachru, Shamit (Stanford University) Sharpe, Eric (Urbana-Champaign) Kapustin, Anton (California Institute of Technology) Silverstein, Eva (Stanford University) Karch, Andreas (University of Washington) Taylor, Washington (MIT) Katz, Sheldon (University of Illinois at Urbana- Van Raamsdonk, Mark (University of British Columbia) Champaign) Walcher, Johannes (UC-Santa Barbara) Kutasov, David (University of Chicago) Witt, Don (University of British Columbia) Liu, Hong (Rutgers University) Zaslow, Eric (Northwestern University) 5 Scattering and Inverse Scattering March 22–27, 2003 Organizers: Richard Froese (University of British Columbia) Gunther Uhlmann (University of Washington) In the fields of scattering and inverse scattering theory techniques of microlocal analysis, including the use of eikonal equations and of complex geometrical optics solutions to Schrödinger and other equations, has led to substantial progress in recent years. The purpose of the workshop was to bring together people working on different aspects of these fields, to appraise the current status of development and to encourage interaction between mathematicians and scientists and engineers working directly with the applications of scattering and inverse scattering. For details, please refer to the report online: http://www.pims.math.ca/birs/workshops/2003/03w5037/report03w5037.pdf Participants: Ammari, Habib (Ecole Polytechnique) Lamoureux, Michael (University of Calgary) Bal, Guillaume (Columbia University) Lin, Chi-Kun (National Cheng Kung University) Colton, David (University of Delaware) Margrave, Gary (University of Calgary) Dobranski, Michael (University of Kentucky) Mazzeo, Rafe (Stanford University) Donaldson, Roger (University of British Columbia) McDowall, Stephen (Western Washington University) Dorn, Oliver (Universidad Carlos 3 de Madrid) Perry, Peter (University of Kentucky) Finch, David (Oregon Sate University) Ramaseshan, Karthik (University of Washington) Frigyik, Bela (University of Washington) Rundell, William (Texas A&M) Froese, Richard (University of British Columbia) Ryzhik, Lenya (University of Chicago) Gibson, Peter (University of Calgary) Salo, Mikko (University of Washington) Graham, Robin (University of Washington) Skokan, Michal (University of Washington) Grossman, Jeff (University of Calgary) Stefanov, Plamen (Purdue University) Hansen, Soenke (Universitaet Paderborn) Sá Barreto, Antônio (Purdue University) Herbst, Ira (University of Virginia) Tamasan, Alexandru (University of Toronto) Hislop, Peter (University of Kentucky) Uhlmann, Gunther (University of Washington) Hitrik, Michael (MSRI) Vodev, Georgi. (Université de Nantes) Isakov, Victor (Wichita State University) Wang, Jenn-Nan (National Taiwan University) Ivrii, Victor (University of Toronto) Weder, Ricardo (Universidad Nacional Autonoma de Kirsch, Andreas (Universität Karlsruhe) Mexico) Kusiak, Steven (University of Washington) Yedlin, Matt (University of British Columbia) 6 Noncommutative Geometry March 22–27, 2003 Organizers: Alain Connes (Institut des Hautes Etudes Scientifiques) Masoud Khalkhali (University of Western Ontario) Joachim Cuntz (Universitat Muenster) Boris Tsygan (Pennsylvania State University) George Elliott (University of Toronto) Noncommutative geometry is a rapidly grow- ing new area of mathematics with links to many disciplines in mathematics and phys- ics. This is a highly interdisciplinary sub- ject which draws its intuitions, ideas and methods from various
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