## Rigidity for von Neumann algebras of amalgamated free product groups

#### Adrian IoanaUniversity of California, San Diego (UCSD)

I will explain recent work with Ionut Chifan in which we provide a large family of amalgamated free product groups whose amalgam structure can be completely recognized from their von Neumann algebras. Our result significantly strengthens some of the previous Bass-Serre rigidity results for von Neumann algebras. As a consequence, we obtain the first examples of amalgamated free product groups which are W$^*$-superrigid.

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