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SUMMARY:"Geometric methods in representation theory  of finite groups of L
 ie type"
DTSTART:20150325T111500
DTEND:20150325T121500
DTSTAMP:20260917T132144Z
UID:ca0501e2802ddf41e881f2baf52b74d42e5ae5e77d35dc90b2e78bf9
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Olivier DUDAS (Université Paris Diderot)\nFinite groups
  of Lie type\, also called finite reductive groups\, are the finite analog
 s of complex Lie groups. Examples of such groups include the classical gro
 ups (finite linear groups GL_n(q)\, orthogonal groups SO_n(q)\, symplectic
  groups Sp_{2n}(q)) and the so-called exceptional groups.\nSuch finite gro
 ups have an underlying geometric structure\, making geometric methods part
 icularly adapted to study their symmetries and their representation theory
 . Following this observation\, Deligne and Lusztig introduced in the 70's 
 a family of algebraic varieties acted on by finite groups of Lie type. One
  goes from the world of algebraic varieties to the world of linear algebra
  by considering the cohomology of these varieties\, which yields linear re
 presentations of finite groups of Lie type.\nAlthough Deligne-Lusztig vari
 eties are similar to flag varieties and Grassmannians\, little is known ab
 out their cohomology and the representations they afford. Nevertheless\, t
 here is a lot of evidence that they encode most of the representation theo
 ry of finite groups of Lie type.\nStarting with the example of SL_2(q)\, o
 ne of the smallest non-trivial finite groups of Lie type\, I will present 
 conjectures and recent results illustrating how rich the cohomology of the
 se varieties is\, and what has yet to be discovered.
LOCATION:BI A0 448 https://plan.epfl.ch/?room==BI%20A0%20448
STATUS:CONFIRMED
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