7 problems

A finite-volume hyperbolic manifold is a manifold equipped with a complete finite-volume hyperbolic metric; its fundamental group is cubulated if it acts properly and cocompactly o…

A group is cubulable if it acts properly and cocompactly on a median graph, and it is acylindrically hyperbolic if it admits a non-elementary acylindrical action on a hyperbolic sp…

A group is cubulable if it acts properly and cocompactly on a median graph. For $n\geq 1$, $(\mathrm{FW}_n)$ denotes the fixed-point property for actions on median graphs of cubica…

Let $\Gamma$ be a convex cocompact subgroup of $\mathrm{PO}(n,1)=\mathrm{Isom}(\mathbb{H}^n)$, where $\mathbb{H}^n$ is real hyperbolic $n$-space. Such a subgroup is noncubulated if…

Let $W_{\Gamma}$ be a right-angled Coxeter group. A cubical coarse median rigidity conjecture. 1. There are only finitely many cubical coarse median structures on $W_{\Gamma}$. 2.…

Cubulation conjecture. Assume that either $n \leq 3$ or that $M$ is arithmetic of simplest type. Then, for every $\lambda > 1$, there is a compact cubical model $X$ such that there…

Let $M$ be the $3$-manifold under consideration, and let $\pi_1M$ denote its fundamental group. The group $\pi_1M$ acts freely and cocompactly on a CAT(0) cube complex if the actio…