K-Theory of Group C*-Algebras and Applications

Explore a 70-minute lecture from Professor Gennadi Kasparov of Vanderbilt University, delivered at Kyoto University, examining the fascinating evolution and current state of K-theory for group C∗-algebras. Delve into its significant applications in topology of smooth manifolds, particularly the Novikov conjecture on higher signatures, and representation theory of semisimple Lie groups. Discover the deep connections between K-theory and index theory of elliptic operators, while learning about major unsolved challenges like the Baum-Connes and Kadison-Kaplansky conjectures. Designed to be accessible for graduate students with basic knowledge of Hilbert space theory, gain insights into this rapidly developing field that has seen remarkable progress over the past four decades.