Mathematisches Kolloquium

Abstract: Groups like GLn, SLn or SPn play an important role in many areas of mathematics. Some of their properties (when studied over the real or complex numbers) can be understood via the associated symmetric spaces. Jacques Tits introduced buildings as a tool to study the respective groups over other fields and developed, together with Francois Bruhat, a theory that also captures non-archimedian local fields with discrete valuation, like the p-adic numbers. Buildings have since been used in many contexts and serve as prime examples of non-positively curved metric spaces. In this talk I will explain how some of the subgroup structures of such groups G can be explained using combinatorial and geometric properties of the associated Weyl groups and (affine) Bruhat-Tits buildings. Buildings, for example, simultaneously encode (affine) flag varieties and (affine) Grassmannians. I will present two examples highlighting the connection between geometric structures of the building and/or the Weyl group and certain algebraic properties of G: an analog of Kostant's classical Convexity theorem in the non-archimedian setting and the computation of dimensions of affine Deligne-Lusztig varieties by means of combinatorial data.

Donnerstag, den 27. April 2023 um 17:15 Uhr, in Mathematikon, INF 205, HS Donnerstag, den 27. April 2023 at 17:15, in Mathematikon, INF 205, HS

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. P. Albers