8 problems

Let $\Gamma$ be a higher-rank lattice and let a character mean the character object considered in the source. Connes' character rigidity conjecture. Every character of $\Gamma$ is…

Let $\Gamma$ be an irreducible higher-rank lattice. The charfiniteness conjecture. The group $\Gamma$ is charfinite, in the sense of the character-rigidity terminology used in the…

Let $\Gamma$ be an irreducible higher-rank lattice, and let a URS mean a minimal subsystem of the space of subgroups of $\Gamma$ with the Chabauty topology. The URS rigidity conjec…

Let $\Gamma$ be a center-free irreducible higher-rank lattice. Stuck–Zimmer's IRS rigidity conjecture. For every ergodic probability-measure-preserving action of $\Gamma$ on a prob…

Let $\Gamma$ be an irreducible higher-rank lattice. Lubotzky's property $\tau$ conjecture. The group $\Gamma$ has property $\tau$. This is listed among consequences of the spectral…

Let $\Gamma$ be a center-free irreducible higher-rank lattice in $G$, and let $V$ be a unitary representation of $\Gamma$ whose action does not extend to a $G$-action on any non-tr…

Let $\Gamma$ be a center-free irreducible higher-rank lattice in $G$, and let $V$ be a unitary representation of $\Gamma$. Assume that the $\Gamma$-action on $V$ does not extend to…

Let $G$ be a higher-rank semisimple Lie group, let $\Gamma$ be a higher-rank lattice in $G$, and let $r(G)$ be the root-theoretic dimension defined in the source. Let $M$ be a mani…