April 18th, 2023

Date:
April 18, 2023

Speaker:
Wolfgang Lück (University of Bonn)

Title
On the FarrellJones Conjecture
Abstract
I will give a nontechnical gentle survey over the FarrellJones Conjecture and its application. It aims at the computation of the algebraic K and Lgroups 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 nontrivial 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 FarrellJones Conjecture for the Hecke algebra of reductive padic 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 GetTogether 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

Place:
KA