** "Geometry and Analysis on Groups" Research Seminar **

**Time:** 2015.04.28, 15:00--17:00

**Location:** Seminarraum 8, Oskar-Morgenstern-Platz 1, 2.Stock

**Title:** Geometric Examples of the Baum-Connes conjecture and Langlands
duality.

**Speaker:** Nick Wright (University of Southampton)

**Abstract:**
The Baum-Connes conjecture asserts that two invariants of a
group are isomorphic: the first is a geometric invariant, the
K-homology of the classifying space; the second is an analytic
invariant, the K-theory of the group \(C^*\)-algebra. In some (rare)
examples the second invariant can also be viewed geometrically. In this
talk I will show that even when the group \(C^*\)-algebra can be viewed
geometrically, its geometry may be different to that of the classifying
space. In the case of (extended) affine Weyl groups the geometries are
linked by Langlands duality and the Baum-Connes assembly map can
therefore be viewed as a form of Langlands duality.