Classification of arithmetic hyperbolic reflection groups

Géométrie Dynamique

Salle Duhem M3
Nikolay V. Bogachev
Moscow Institute of Physics and Technology
Vendredi, 26 Avril, 2019 - 11:15 - 12:15

Due to results of Vinberg (1967-1984), Nikulin (1980s, 2007), Agol, Belolipetsky and other mathematicians (2005-2008) it is known that there are only finitely many maximal arithmetic hyperbolic reflection groups in all dimensions. However, the problem of its classification (posed, in fact, by Vinberg in 1967) is still very far from being completely solved. In this talk I will describe the known classification results and geometric approaches for solving this problem, and also I will present my recent results on the classification of stably reflective hyperbolic lattices of rank 4 and a software implementation of Vinberg's algorithm.