RIGIDITY FOR VON NEUMANN ALGEBRAS

By Adrian Ioana. International Congress of Mathematicans, 2017

62 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a6b0d1f57b47e0344e7481871fd8af3a13a91b66

Citations in the corpus

• A random matrix approach to the Peterson-Thom conjecture (2020, unknown): “See [64, 67, 68, 38, 39] for further results, including resolutions”