Algebraic Groups, Finite Groups, Geometries, Representations

50 years of Chevalley Seminar

CIRM, Luminy, France

22 September 2014 - 26 September 2014

Preliminary list of Speakers

Every algebraist acknowledges the fundamental contribution of the Chevalley Seminar of the years 1956-59 classifying reductive groups soon after Chevalley's paper giving a construction of finite simple groups of Lie type (Tohoku, 1955). This establishes a strong connexion between finite groups and algebraic groups. It will be completed with the theory of group schemes already sketched by Grothendieck in the same seminar, and on the other hand by the program of classification of finite simple groups. Chevalley himself chose this latter theme as the main subject when restarting his seminar at the end of the sixtees (Vincennes, Institut Henri Poincaré). The seminar has continued its activity after the death of Chevalley (1984) until today and one can now count fifty years of the seminar. See the current programme.

Chevalley's themes (reductive groups, reflection groups, flag varieties) are still central in algebra. New methods and notions, such as l-adic cohomology, derived module categories, or braid groups, all give new insights on the geometry and representations of finite groups, p-adic groups and associated algebras.

The so-called perverse equivalences took inspiration from works on representations of groups of Lie type and lead to new questions and conjectures on the homology of Deligne-Lusztig varieties.

Many conjectures of global-local type in the representation theory of finite groups (McKay, Alperin) have been recently reduced to related statements on finite quasi-simple groups. The classification of finite simple groups helps then reducing essentially to questions about Chevalley groups.

Langlands' program, starting with groups over local rings, also leads to questions about their finite analogues.

The conference organized in Luminy (Sep 22-26, 2014) will gather experts in the fields mentioned above, along with speakers, organizers and attendants of the Chevalley Seminar.

Organizers: Olivier Brunat, Marc Cabanes, Radha Kessar