## EVENT DETAILS AND ABSTRACT

**Noncommutative Geometry**
**Title:** Geometric structure in the representation theory of p-adic groups

**Speaker:** Professor Paul Baum

**Speaker Info:** Penn State

**Brief Description:**

**Special Note**:

**Abstract:**

Let G be a reductive p-adic group. G is locally compact so G has the usual
unitary representation theory of locally compact groups. For number
theory,
Langlands program etc, however, the relevant representations are the
smooth representations. This talk states a conjecture --- due to
A.M.Aubert, P.Baum and R.Plymen --- which states that the smooth dual
of G (i.e. the set of isomorphism classes of irreducible smooth
representations of G) is a countable disjoint union of complex affine
varieties. These varieties are explicitly identified. The conjecture
is very closely connected to work of J.Bernstein and is based on
calculations of the periodic cyclic homology of affine Hecke algebras.
This talk is algebraic and might be viewed as non-commutative algebraic
geometry. However, there is some interaction with the usual unitary
representation theory of G.

**Date:** Tuesday, April 17, 2007

**Time:** 3:00pm

**Where:** Lunt 101

**Contact Person:** Boris Tsygan

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

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

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