This three-year award supports cooperative research in operator K-theory and representation of p-adic groups between Paul Baum and Nigel Higson, Pennsylvania State University, and Roger Plymen from the University of Manchester in the United Kingdom. The objective of this project is to determine the validity of the Baum-Connes conjecture using the case of semi-simple, p-adic algebraic groups. The investigators will also explore the conjecture's relationship to index theory for Euclidean buildings and to Kutsko's conjecture for semi-simple, p-adic groups. The proposed research will advance our understanding of the K-theory of C* algebras associated with p-adic groups. By bringing together results from the number theory, analysis, topology and group representation theory, K-theory provides an adequate framework for expressing and unifying results in these fields. This project will benefit by combining Baum and Higson's geometric viewpoint and experience on K-theory and index theory with Plymen's work on representational theory and algebraic (p-adic) groups.
