3 problems

Let $G$ be an amenable group, and let $\lambda_G$ denote its left regular representation. An affine action of $G$ with linear part $\lambda_G$ has an affine action map whose linear…

Let $G=G_1\times\cdots\times G_k$ be a semisimple Lie group whose factors are all non-compact, let $\Gamma<G$ be an irreducible lattice, and let $\rho$ be an affine action of…

Let $G$ be a Gromov hyperbolic group, and consider affine actions of $G$ on a Hilbert space whose linear parts are uniformly bounded representations. An affine action is proper whe…