Global/Local Conjectures in Representation Theory of Finite Groups

The Banff International Research Station will host the "Global/Local Conjectures in Representation Theory of Finite Groups" workshop from March 16th to March 21st, 2014.

Group Theory is essentially the theory of symmetry for mathematical and physical systems, with major impact in diverse areas of mathematics. The Representation Theory of Finite Groups is a central area of Group Theory, with many fundamental problems, starting from a list of several deep conjectures formulated by Richard Brauer in 1963, and including subsequent conjectures of John McKay, Jonathan Alperin, Michel Broue, and others. Many of these conjectures relate global and local properties of finite groups, and all of them remain open up to date. The classification of finite simple groups raised the hope that one should be able to reduce some of the aforementioned conjectures to various statements about simple groups and thus provide a way to prove the conjectures. This hope has recently materialized when several of these conjectures have been reduced to questions about finite simple groups, by work of M. Isaacs, Malle, and G. Navarro, Navarro and P.H. Tiep, and B. Sp"ath). The proposed meeting will bring together the leading experts and young researchers in the representation theory of finite groups and algebraic groups to exploit the substantial recent advances on these fundamental conjectures and facilitate significant progress along the lines of all of them. We expect that by the time of the meeting, further substantial progress on the remaining steps towards proving these conjectures will have been achieved.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).

BIRS Scientific Director, Nassif Ghoussoub
E-mail: birs-director[@]birs.ca
http://www.birs.ca/~nassif