Graduiertenkolleg ``Gruppen und Geometrie''
S O M M E R S C H U L E
"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.
University of Orleans
Prof. Paul Baum
Pennsylvania State University
"Topological K-theory and C*-algebras"
"Geometric approaches to the Baum-Connes conjecture"
"p-adic groups and the
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