4 problems

Let $\operatorname{\mathsf{G}}$ be a connected semisimple Lie group without compact factors and with finite center. Suppose $\Gamma<\operatorname{\mathsf{G}}$ is a Zariski dense di…

Bekka–Valette conjecture. There exist unitary representations of $\Gamma$ that are not weakly contained in any representation restricted from $G$.

Let $G$) be a semisimple Lie group, either real or $p$-adic, and let $\Gamma$ be a cocompact lattice in $G$. Valette's conjecture. The group $\Gamma$ has the Rapid Decay property.…

Let $H$ be a semisimple Lie group of type $\mathrm{A}_1$ with more than one simple factor, and let $\mathrm{IL}_{H}(x)$ denote the maximal size of a family of pairwise isospectral,…