Classification and rigidity for von Neumann algebras

Abstract

In this talk, I will survey recent progress made on the classification of von Neumann algebras arising from countable groups and their actions on probability spaces. In particular, I will present the first results which provide classes of (superrigid) groups and actions that can be entirely reconstructed from their von Neumann algebras.

To appear in Proceedings of the 6th European Congress of Mathematics (Krakow, 2012)