7 problems

Let $APrism_m$ be the $m$-parameter antiprism, and let $Prism(APrism_m)$ denote the prism over it. Write $z$ for the zigzag vector and $Int$ for intersection vectors. Prism-over-an…

Let $C_p$ and $C_q$ be polygons, and set … Write $z$ for the multiset of zigzag lengths and multiplicities, and $Int$ for intersection vectors. Product-of-polygons conjecture. For…

Let $f:\Delta_X\rightarrow\Delta_B$ be a surjective morphism of rational conical polyhedral complexes such that $f^{-1}(0)=\{0\}$. A projective subdivision replaces the complexes b…

Let $P$ be a planar polyhedral complex, and let F=\max\{n\mid\text{\rm {there is an n-gon in }}P\}. Let $k$ and $r$ be the parameters in the spline-dimension formula of Theorem…

Let $X$ be a locally finite polyhedral complex, let $G=\operatorname{Aut}(X)$, and let $\Gamma$ be a nonuniform lattice in $G$. Non-finite presentability conjecture. The group…

Let $X$ be a right-angled hyperbolic building, let $G=\operatorname{Aut}(X)$, and let $\Gamma$ be a nonuniform lattice in $G$. Non-finite generation conjecture. The group $\Gamma$…

Higher-dimensional Balinski-type connectivity conjecture. The graph ${\mathcal G}_k({\mathcal C})$ is