Are Austad: Compact quantum metric spaces and groups of polynomial growth

Abstract: Around 25 years ago Rieffel introduced the notion of a compact quantum metric space, which has put convergence results in high-energy theoretical physics on a solid mathematical foundation. Since then the field has seen a plethora of new techniques and examples. We give an introduction to the theory of compact quantum metric spaces, with a particular focus on how to obtain such objects from discrete groups. We will take the point of view that compact quantum metric spaces are operator systems admitting finite-dimensional approximations in a sense we will make precise. 
Towards the end of the talk, I will report on recent joint work with Jens Kaad and David Kyed on how to metrize crossed products using groups of polynomial growth.
No prior knowledge of compact quantum metric spaces will be assumed.