Dynamics Seminar

Event Information Systoles, commensurability classes and quasi-arithmeticity of hyperbolic reflective orbifold
14:10 on Monday January 22, 2024
15:00 on Monday January 22, 2024
BA6183, Bahen Center, 40 St. George St.
Nikolay Bogachev

University of Toronto Scarborough

In the first part of the talk I will give a short intro to Vinberg's theory of hyperbolic reflection groups. 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 and systoles of the associated reflective orbifolds (i.e. quotients of H^n by such reflection groups). We will also discuss the notion of quasi-arithmeticity introduced by Vinberg in 1967, which has recently become a subject of active research. The talk is based on a series of joint papers with S. Douba, A. Kolpakov, J. Raimbault, Kh. Yorov in different combinations.