April 18, 2023

Wolfgang Lück (University of Bonn)

Title

On the Farrell-Jones Conjecture

Abstract

I will give a non-technical gentle survey over the Farrell-Jones Conjecture and its application. It aims at the computation of the algebraic K- and L-groups of group rings of discrete groups, which are computed in terms of equivariant homology groups of certain classifying spaces. It has many applications to prominent problems in topology, geometry, and algebra. Examples are the Borel Conjecture, which predicts the topological rigidity of closed aspherical manifolds, and the Idempotent Conjecture, which predicts that the complex group ring of a torsionfree group has no non-trivial idempotents. The Conjecture is known for instance for hyperbolic and CAT(0)-groups. Its proof uses methods from equivariant homotopy theory, controlled topology, dynamical systems, and geometric group theory. At the very end I will report on a recent formulation and proof of Bartels and myself of a version of the Farrell-Jones Conjecture for the Hecke algebra of reductive p-adic groups which is of great interest to the theory of smooth representations of such groups.
 

Schedule

10:00 - 11:30 RTG Lecture 1 (Zachary Greenberg), SR 2.058

11:30 - 12:00 Get-Together with speaker, SR 2.058

12:00 - 13:00 Common lunch

13:00 - 13:30 Informal meeting of PhD students, room 1.062

13:45 - 14:45 RTG colloquium: Wolfgang Lück, SR. 1067

14:45 - 15:30 Common tea, Faculty meeting room 1.058

15:30 - 17:00 RTG Lecture 2 (Julia Heller), SR 1.067

KA