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

I discuss the set of rates of growth of a finitely generated group with respect to all its finite generating sets. In a joint work with Sela, for a hyperbolic group, we showed that the set is well-ordered, and that every real number can be the rate of growth of at most finitely many generating sets up to automorphism of the group.