D01 Amenable dynamics via C*-algebras

Three regularity properties and their interplay have been at the heart of exciting recent developments in the structure and classification theory of nuclear C*-algebras: finite nuclear dimension, tensorial absorption of the Jiang–Su algebra, and strict comparison of positive elements. There are corresponding properties for group actions; we will study these dynamic regularity properties in order to gain new insights into amenable groups and their actions, and on rigidity properties of their associated C*-algebras. Taking a dual viewpoint, we will study - and to some extent classify - Cartan subalgebras of C*-algebras. These are maximal abelian subalgebras, the position of which encapsulates crucial information about the underlying dynamics of a C*-algebra.