Mathematisches Institut
Georg-August-Universität Göttingen

Graduiertenkolleg ``Gruppen und Geometrie''



"K-theory of C*-algebras and the Baum-Connes conjecture"

May 22 - May 25,  2002

There will be three lecture series of 4-5 talks.
Prof. Pierre Julg

University of Orleans

Prof.Guoliang Yu

Vanderbilt University

Prof. Paul Baum

Pennsylvania State University 


"Topological K-theory and C*-algebras"



"Geometric approaches to the Baum-Connes conjecture"


"p-adic groups and the
Baum-Connes conjecture"

Summary (preliminary):

This course will be an introduction to topological K-theory for (group) C*-algebras and the main conjecture in this field. This conjecture, due to P. Baum and A. Connes, states that there is a natural isomorphism   KG* (EG) -> K*top (C* (G))  between the equivariant K-homology of the classifying space EG for proper G-actions and the topological K-theory of the reduced C*-algebra of a group G.

Pierre Julg  will start with some of the background material, including an introduction to C*-algebras and their K-theory. He will explain an analytic description of K-homology and describe the Baum-Connes map. Positive and negative results concerning the Baum-Connes conjecture will be stated.

Guoliang Yu  will describe how geometric ideas give rise to similar conjectures in other contexts, which can be used to prove cases of the original Baum-Connes conjecture.

Paul Baum will introduce into the theory of p-adic groups. He will then focus on the special techniques and results available about the Baum-Connes conjecture for p-adic groups. In particular, he will explain how to pass from discrete groups (covered by the other two lecture series) to topological groups.

The summer school addresses in particular graduate students (or soon to be graduate students) and mathematicians who recently got their PhD. The aim is not to address specialists, but introduce into an exciting and active area of research.

We may be able to offer support for a limited number of participants, in particular PhD students. For further details please contact Thomas Schick .