Algebra Seminar: Schwer -- Building bridges between geometry and algebra

Petra Schwer (Otto von Guericke Universitat Magdeburg) 

Friday 16 August, 12-1pm, Place: Carslaw 375 

Title: Building bridges between geometry and algebra 

Abstract: Reductive groups, like GL_n, SL_n, SP_n, play an important role in many areas
of mathematics.  In this talk I will explain how much of the subgroup structure of a
reductive group over a non-Archimedian local field can be explained via the geometry of
an (affine) Bruhat-Tits building, its apartments and retractions.  The building for
example simultaneously encodes the (affine) flag variety and (affine) Grassmannian
associated to the group.  But it also permits to explain more complicated structures
such as representation theoretic data or other associated varieties (e.g.  the affine
Deligne-Lusztig varieties) in purely combinatorial terms.