Baby NCG seminar: Cyclic homology and Fourier theory

Tyrone Crisp

The first part of the talk will be an introduction to cyclic homology, from a C*-friendly point of view. I will explain how cyclic homology provides a natural home for invariants of K-theory classes. In the case of group algebras, these invariants are related to characters of representations, and one can use cyclic homology to study the
interaction between conjugacy classes and representations, extending the well-known theory for finite groups. I will illustrate with the example of affine Weyl groups.