6 problems

Standard-action conjecture. Every quasi-action by $\Gamma$ on a Gromov hyperbolic metric space either has an invariant horoball or is standard.

Finiteness conjecture. If $\Gamma$ is an irreducible lattice in a higher rank Lie group (or in a nontrivial product of locally compact groups) $G$, there are finitely many Gromov h…

Let $n$ be the dimension parameter, let $\rho=(n-1)/2$, and define … where $F(a,b;c;z)$ is the hypergeometric function and $k$ is complex. The zero-free region conjecture. For ever…

Let $n$ be the dimension parameter, let $\rho=(n-1)/2$, and let $F(a,b;c;z)$ denote the hypergeometric function. For the function $F_k(z)=F(k,-\rho;k+n/2;z)$, with complex variable…

Strong Property (T) action conjecture. Any action of $G$ by isometries on $X$ is elementary.

Let $A_S$ be an irreducible non-cyclic FC type Artin group, and let ${\mathcal{CP}_{A_S}}$ denote its complex of parabolic subgroups. Hyperbolicity and infinite-diameter conjecture…