## Quasi-isometry and commensurability for right-angled Coxeter groups

Anne Thomas (Glasgow)

Abstract

Let G be a finite simple graph with vertex set S. The associated right-angled Coxeter group W(G) is the group with generating set S, and relations s^2 = 1 for all s in S and st = ts if and only if s and t are adjacent vertices. We investigate the classification of certain W(G) up to quasi-isometry, which is a "coarse" equivalence relation on finitely generated groups formulated by Gromov, and also up to commensurability, where two groups G and H are commensurable if they have isomorphic finite index subgroups. Our methods are geometric and topological. This is joint work with Pallavi Dani (Louisiana State University) and Emily Stark (Tufts University).