Hang Wang: A K-theoretic approach to semisimple Lie groups and their lattices

Abstract

Semisimple Lie groups and their lattices are of interest in many areas such as differential geometry, number theory, ergodic theory and geometric group theory. In this talk, we propose an operator K-theory framework to study the groups and their K-theoretic functoriality, also motivated by the Baum-Connes conjecture for such pairs of groups. In the case of a uniform lattice, we find a cohomological interpretation of the Selberg trace formula involving the K-theory of the maximal group \(\mathrm{C}^*\)-algebras of a semisimple Lie group and its lattice. As an application, this implies the index theoretic version of the Selberg trace formula developed by Barbasch and Moscovici, in this special case of a uniform lattice. This is joint work with Bram Mesland and Mehmet Haluk Sengun.