Arithmetic hyperbolic reflection groups

TL;DR

This survey reviews recent advances and open problems in the study of arithmetic hyperbolic reflection groups, which are discrete groups generated by reflections in hyperbolic polyhedra.

Contribution

It summarizes recent results from the last ten years and highlights open problems in the field of arithmetic hyperbolic reflection groups.

Findings

Recent classifications and structures identified

New open problems proposed in the field

Progress made in understanding group properties

Abstract

A hyperbolic reflection group is a discrete group generated by reflections in the faces of an $n$-dimensional hyperbolic polyhedron. This survey article is dedicated to the study of arithmetic hyperbolic reflection groups with an emphasis on the results that were obtained in the last ten years and on the open problems.