Haluk Şengün

A K-theoretic Selberg trace formula

The close relationship between index theory and representation theory is a classical theme. In particular, the trace formula has been studied through the lens of index theory by several researchers already. In joint work with Bram Mesland (Nijmegen) and Hang Wang (Shanghai), we take this connection further and obtain a formulation of the trace formula in K-theoretic terms. The central object here is the K-theory group of the C*-algebra associated to a locally compact group. This work is part of a program which explores the potential role that operator K-theory could play in the theory of automorphic forms.