3 problems

Let $G$ and $H$ be finite graphs that are $K$-roughly isometric, and suppose both have maximal degree at most $d$. Denote by $\tau_{\infty}(G)$ and $\tau_{\infty}(H)$ the…

Let $R=R((p_n),(q_n))$ and $R'=R((p_n'),(q_n'))$ be isotropic trees. Let ${\mathcal{X}}((p_n),(q_n),(p_n'),(q_n'))$ denote the associated set of obstructions to a rough isometric e…

Rough-isometry invariance conjecture. There is a constant $C(K,d)$ such that