Structure of nuclear C*-algebras: From quasidiagonality to classification, and back again

Abstract

I give an overview of recent developments in the structure and classification theory of separable, simple, nuclear C*-algebras. I will in particular focus on the role of quasidiagonality and amenability for classification, and on the regularity conjecture and its interplay with internal and external approximation properties.

20 pages; intended for Proceedings of ICM 2018