Topology and Analysis: Complementary approaches to the Baum-Connes and Novikov conjectures

The proposers are presently the recipients of a Focused Research Group grant from NSF on this topic. The summer of 2003 would be the final one funded by thegrant and it would be particularly appropriate to have a summer school on the topic to survey the work done over thethree years of the grant and to formulate the next set of problems which will be worked on. There have been a series of summer schoolsand training session in Europe over the past few years on this topic and while senior researchers from Canada and US have been able to participate, there has been less opportunity for younger mathematicians and graduate students from North (or South) America to take part. A program as we are requesting would contribute to changing that situation.

The specific objectives of the workshop would be to merge more closely the the geometric and analytic approaches to the study of discrete groups from the point of view of the Novikov conjecture. The analytic approach is based on studying the set of irreducible representations of the fundamental group of a manifold as a dual object for the group. The geometric approach is based on Gromov's notion of asymptotic properties of groups. While some connections have been made, there is much remaining to be developed. Currently under the Focused Research Grant work is proceeding well, but it has proved fruitful to continue to bring together workers in these different aspects. The dynamics of the action of the group on various spaces has also started to play an increasingly important role. A meeting like the one being proposed would bring together people who already are acquainted, but the informality of the activities and the extendedperiod would be likely to solidify collaborations and continue to establish a subject in its own rite.

It should be emphasized that the lectures given would be expository and aimed at educating both graduate students andyoung researchers, (as well as senior scientists) in less familiar aspects of the subjects. In particular, we would have a lecture series on Group C*-algebras and Connections with Dynamics,and one on Geometric Group Theory and connections with Noncommutative Geometry.

Confirmed Participants