4 problems

Let $A_\Gamma$ be an Artin group, let $C_\Gamma$ be its associated clique-cube complex, and let … be the action by left multiplication. For a subgroup $H\subset A_\Gamma$, write…

A group $G$ has property ${\rm F}\mathcal{C}'$ if every cellular action of $G$ on a finite-dimensional CAT$(0)$ cube complex is locally elliptic. A subgroup is non-trivial if it is…

Let $G$ be a group acting geometrically on a CAT(0) cube complex. A group is cyclically hyperbolic if it admits a non-elementary acylindrical action on a hyperbolic space with a lo…

Wise's conjecture. Every torsion-free one-relator group with no subgroup isomorphic to $BS(m,n)$, for $m\neq\pm n$, acts freely on a CAT(0) cube complex.