Amenability Beyond Groups: Dynamics and Operator Algebras

Amenability is a classical notion originating in group theory, closely related to invariant means and paradoxical decompositions. In operator algebra theory, amenability reappears in different forms, most notably as nuclearity for C*-algebras and injectivity for von Neumann algebras.
In this talk, I will discuss how amenability extends beyond groups to dynamical systems given by actions on C*-algebras, and how it governs structural properties of the associated crossed products. I will explain how several approximation properties provide equivalent characterizations of amenable C*-dynamical systems, and how these ideas lead to criteria for nuclearity and for the coincidence of full and reduced crossed products.