Coarse geometry of right-angled Coxeter groups

Ivan Levcovitz (CUNY)

A main goal of geometric group theory is to understand finitely generated groups up to a coarse equivalence (quasi-isometry) of their Cayley graphs. Right-angled Coxeter groups, in particular, are important classical objects that have been unexpectedly linked to the theory of hyperbolic 3-manifolds through recent results, including those of Agol and Wise. I will give a brief background of what is currently known regarding the quasi-isometric classification of right-angled Coxeter groups. I will then describe a new computable quasi-isometry invariant, the hypergraph index, and its relation to other invariants such as divergence and thickness.