4 problems

Let $\Gamma\curvearrowright (X,\mu)$ be a Bernoulli action of an icc group $\Gamma$ with Kazhdan's property (T). The action is W$^*$-superrigid if its isomorphism class as a group…

Superrigidity conjecture. Maximal representations of a complex hyperbolic lattice into a Hermitian Lie group should be superrigid.

Let $\Gamma\curvearrowright (X,\mu)$ be a Bernoulli action of an icc group $\Gamma$ with Kazhdan's property (T). An action is W$^*$-superrigid if every free ergodic probability-mea…

Let $X$ and $Y$ be surfaces, and let $\operatorname{Map}(X)$ and $\operatorname{Map}(Y)$ denote their mapping class groups. Consider a homomorphism … The genus of $X$ is assumed to…