Research Project: We study rigidity phenomena in abstract reflection groups, or Coxeter groups. Two such rigidity phenomena are quasi-isometric rigidity, in which large scale geometric equivalence implies algebraic commensurability, and graphical discreteness, in which admitting geometric actions on a common graph implies virtual isomorphism.

We aim to characterize Coxeter groups with these properties. Because the manifold case is well understood, we are particularly interested in attacking the case of Coxeter groups of pseudo-manifold type. 

Research Team: Christopher Cashen (U Vienna), Pallavi Dani (Louisiana State U, Baton Rouge), Kevin Schreve (Louisiana State U, Baton Rouge), Emily Stark (Wesleyan U)