# The noncommutative geometry of Cuntz-Pimsner algebras

### Bram Mesland (Leibniz University Hannover)

Tuesday 1st March, 2016 16:00-17:00 Maths 522

#### Abstract

The class of Cuntz-Pimsner algebras encompasses a wide range of $C^{*}$-algebras. This includes crossed products by Z, Cuntz-Krieger algebras, Exel crossed products and the three sphere as well as its \theta and q-deformations (the quantum group SU_q(2)). By construction, a Cuntz-Pimsner algebra comes with extra K-theoretic information in the form of an extension of $C*$-algebras. The goal of this talk is to explain how this extension can be understood as an unbounded Kasparov module. In the case of Cuntz-Krieger algebras, this can be done based on the relation of shift tail equivalence of the associated subshift of finite type. This dynamical systems picture generalises, under suitable conditions, to other Cuntz-Pimsner algebras, and allows us to understand their noncommutative geometry in dynamical terms.

This is joint work with Magnus Goffeng and Adam Rennie