URegina-PIMS Distinguished Lecture: Stefaan Vaes

The theme of this lecture is the dichotomy between amenability and non-amenability, both in operator algebras and ergodic theory. I will review the fundamental classification results for amenable von Neumann algebras due to Connes and Haagerup. Then I will focus on the nonamenable case, where Popa's deformation/rigidity theory has led to striking rigidity theorems for von Neumann algebras associated with groups and actions of groups on measure spaces. I will survey some recent results, including the computation of invariants of II₁ factors and the challenging problem of deciding when II₁ factors can be embedded one into the other.

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