Rigidity for von Neumann algebras – Adrian Ioana – ICM2018

Analysis and Operator Algebras
Invited Lecture 8.5
Rigidity for von Neumann algebras
Adrian Ioana

Abstract: We survey some of the progress made recently in the classification of von Neumann algebras arising from countable groups and their measure preserving actions on probability spaces. We emphasize results which provide classes of (W^*-superrigid) actions that can be completely recovered from their von Neumann algebras and II_1 factors that have a unique Cartan subalgebra. We also present cocycle superrigidity theorems and some of their applications to orbit equivalence. Finally, we discuss several recent rigidity results for von Neumann algebras associated to groups.

ICM 2018 – International Congress of Mathematicians ©
 
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