University of Sydney Algebra Seminar

Petra Schwer (Otto von Guericke Universitat Magdeburg)

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

Building bridges between geometry and algebra

Reductive groups, like \(GL_n\), \(SL_n\) or \(SP_n\), 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.