Motivated by questions concerning the rigidity of certain von Neumann
algebras associated to groups or group actions, Boutonnet, Ioana and Peterson
recently introduced the notion of proper proximality of a countable group. I will
describe this notion and the motivations behind it, and explain how techniques from
geometric group theory can be used to show that certain nonpositively curved groups,
including rank one CAT(0) groups and mapping class groups, are properly proximal.
This is a joint work with Jingyin Huang and Jean Lécureux.