Geometry and Topology Seminar

Nikolay Bogachev, University of Toronto

Commensurability classes and quasi-arithmeticity of hyperbolic reflection groups

In the first part of the talk I will give an intro to the theory of hyperbolic reflection groups initiated by Vinberg in 1967. Namely, we will discuss the old remarkable and fundamental theorems and open problems from that time. The second part will be devoted to recent results regarding commensurability classes of finite-covolume reflection groups in the hyperbolic space H^n. We will also discuss the notion of quasi-arithmeticity (introduced by Vinberg in 1967) of hyperbolic lattices, which has recently become a subject of active research. The talk is partially based on a joint paper with S. Douba and J. Raimbault.

MC 5417