Appears in collection : 2022 - T2 - WS3 - Hyperbolic groups and their generalisations

In this talk we will discuss the relation between the volume of a quotient X/G of a (Gromov) hyperbolic space X by a group G acting freely and cocompactly on X, and the "complexity" of the group G. We will then see how to use this relation to study finite-index subgroups of cubulated hyperbolic groups.