When is a RACG QI to a RAAG

Tim Susse (Bard College at Simon's Rock)

Abstract: A celebrated theorem of Davis and Januszkiewicz shows that every right-angled Artin group is commensurable with some right-angled Coxeter group. The converse, however, is not true and the open question of which RACGs are QI to RAAGs has achieved folk status. In this talk we will discuss the state of the art on this question, which uses some of the most powerful tools in Geometric Group Theory. We will focus on recent results of the speaker, showing that, at low enough density an Erdős-Rényi random RACG is almost surely not QI a RAAG.