9 problems

Let $\Gamma$ be a group acting properly discontinuously and cocompactly on $\mathbb{R}^n$ by affine transformations. Auslander's conjecture. Then $\Gamma$ is virtually solvable. Th…

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…

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 $G_\mathbb{R}$ be a semisimple real Lie group, let $\rho$ be a representation of $G_\mathbb{R}$ on a finite-dimensional real vector space $V$, and let…

Let $G$ be a semisimple real Lie group, let $V$ be a finite-dimensional real vector space, and let $\rho$ be a representation of $G$ on $V$. The paper gives a sufficient criterion…

Let $\mathfrak G$ be a finite groupoid acting affinely on a vector space $V$, and let $\Phi$ denote the affine action. Suppose that all orbits of the action are finite, and let…

Let $\mathfrak G$ be a finite groupoid acting affinely on a vector space $V$, and let $\Phi$ denote this affine action. Assume that every orbit of the action is finite, and let…

Let $G$ be a group of polynomial growth, let an affine action of $G$ have weakly mixing linear part, and let its associated $1$-cocycle be averaged over balls of radius $n$ centere…