## EVENT DETAILS AND ABSTRACT

**Colloquium**
**Title:** Trees, buildings, elliptic operators, and K-theory for group C* algebras

**Speaker:** Professor Paul Baum

**Speaker Info:** Penn State

**Brief Description:**

**Special Note**:

**Abstract:**

Let G be a locally compact Hausdorff topological group. Examples are
Lie groups, discrete groups, p-adic groups, and adelic groups. The (left)
regular representation of G gives rise to a C* algebra known as the
reduced C* algebra of G. Twenty five years ago P.Baum and A.Connes
conjectured an answer to the problem of calculating the K-theory of
this C* algebra. When true, the conjecture has corollaries in various
branches of mathematics. At the present time, there is no known counter-
example and the conjecture has been proved for certain classes of groups.
The search for a counter-example has led to some geometrical issues
involving expander graphs. This talk will explain the conjecture. The
talk is intended for non-specialists. The basic definitions (C* algebra,
K-theory etc.) will be carefully stated.

**Date:** Monday, April 16, 2007

**Time:** 4:00pm

**Where:** Lunt 105

**Contact Person:** Boris Tsygan

**Contact email:** tsygan@math.northwestern.edu

**Contact Phone:** 847-467-6446

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