GeorgAugustUniversität Göttingen Graduiertenkolleg ``Gruppen und Geometrie'' 
S O M M E R S C H U L E
"Ktheory of C*algebras
and the BaumConnes conjecture"
May 22  May 25, 2002
There will be three lecture series of 45 talks.
Prof. Pierre
Julg
University of Orleans 
Prof.Guoliang Yu Vanderbilt University

Prof. Paul Baum Pennsylvania State University

"Topological Ktheory and C*algebras"

"Geometric approaches to the BaumConnes conjecture" 
"padic groups and the

Summary (preliminary):
This course will be an introduction to topological Ktheory 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 Khomology of the classifying
space EG for proper Gactions and the topological Ktheory
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 Ktheory. He will explain an analytic description of Khomology
and describe the BaumConnes map. Positive and negative results concerning
the BaumConnes 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 BaumConnes conjecture.
Paul Baum will introduce into the theory
of padic groups. He will then focus on the special techniques and results
available about the BaumConnes conjecture for padic 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 .