6 problems

Let $\Sigma$ be a compact, connected, orientable surface, and let $\mathcal A$ be a multiarc and curve graph on $\Sigma$. For a witness $W$, let…

Cocompact CAT(0) cube complex conjecture. All cocompact CAT(0) cube complexes are hierarchically hyperbolic.

Relative hyperbolicity classification conjecture. $d4a2$ is relatively hyperbolic if and only if this HHS structure has isolated orthogonality.

Intersection-property conjecture. All hierarchically hyperbolic spaces satisfy the intersection property.

Intersection-property conjecture. Every hyperbolic space admits a hierarchically hyperbolic structure with the intersection property.

Strongly quasiconvexity dichotomy. The strongly quasiconvex subsets of any non-relatively hyperbolic, hierarchically hyperbolic space are either hyperbolic or coarsely cover the en…