4 problems

Gromov's conjecture. Every finitely generated amenable group has no first reduced $\ell^p$-cohomology.

Let $G$ be a non-compact simple group over a local field $F$ with finite center and rank $r$. The twice-the-rank non-vanishing conjecture. For every sufficiently large $p$, … A sim…

Let $G$ be a non-compact semisimple group over a local field $F$ with finite center and rank $r$. The non-uniform lattice extension conjecture. The full statement of Gromov's $L^p$…

Let $G$ be a semisimple Lie group, let $K$ be a maximal compact subgroup, and let $G/K$ be the associated homogeneous space. Write $\operatorname{rank}_{\mathbb{R}}(G)$ for the rea…