Stefaan Vaes
(KU Leuven)
October 6, 2021
Organized by Europe GNCG Seminar.

Superrigidity for dense subgroups of Lie groups and their actions on homogeneous space

An essentially free group action of a discrete group $\Gamma$ on a measure space $(X,\mu)$ is called W*-superrigid if the crossed product von Neumann algebra $L^\infty(X) \rtimes \Gamma$ completely remembers the group $\Gamma$ and its action on $(X,\mu)$. After a brief survey of earlier W*-superrigidity theorems, I will focus on a recent joint work with Daniel Drimbe in which we prove W*-superrigidity for certain dense subgroups of PSL(2,R) acting isometrically on the hyperbolic plane. The main tool is a new cocycle superrigidity theorem for dense subgroups of Lie groups acting by translation.

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