Arithmetic groups and K-theory

Haluk Sengun  (University of Sheffield)

14:00-15:00, Nov 12, 2019   Science Building A510

Abstract:

Cohomology of arithmetic groups, equipped with Hecke operators, play a central role in the Langlands programme. Given an arithmetic group G, there are certain C*-algebras that come naturally associated to G and one can ask whether the K-theory of these C*-algebras could play a role similar to that of the cohomology of G. In this partly expository talk, we will start by introducing arithmetic groups and their cohomology as Hecke modules. After discussing how to equip various K-theory groups associated to arithmetic groups with Hecke operators (this is joint work with Bram Mesland), we will discuss the Matsushima formula and speculate on its implications on the K-theory of groups C*-algebras.

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