4 problems

Small sphere to small gap conjecture. Then $G$ has the SG property. The SG property would provide the ball-intersection control needed for the SBM theory; it is known for…

Let $G$ be a finitely generated virtually nilpotent group with symmetric generating set $S$, and let $S(g,n)$ denote the sphere of radius $n$ about $g$. Suppose that $G$ has polyno…

Let $G$ be a finitely generated virtually nilpotent group, let $S$ be a finite generating set, and let $\mathcal{D}_{G,S}^{sof}$, $\mathcal{D}_{G,S}^{hyp}$,…

A finitely generated group $\Gamma$ is strongly scale-invariant if there exists an embedding $\varphi:\Gamma\hookrightarrow\Gamma$ with image of finite index and such that … is fin…