Growth spectrum of a hyperbolic group

Name: Growth spectrum of a hyperbolic group
Start: 2026-11-13T13:45:00+00:00
End: 2026-11-13T15:00:00+00:00
Location: MR13

Hosted by Geometric Group Theory (GGT) Seminar

Friday 13 November 2026, 13:45

Venue time (London)

MR13

Friday 13 November 2026, 13:45Venue time (London)

Friday 13 November 202613:45 · Venue time (London)

MR13

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Speaker: Rémi Coulon (CNRS, Dijon)
Series: Geometric Group Theory (GGT) Seminar

Given a group G acting properly on a metric space X, the growth rate of this action measures the "size'' of its orbits. The "growth spectrum" of a group G is the set of growth rates of its subgroups (for a fixed action on X). Although the growth rate of an individual subgroup has many connections with other geometric / dynamical objects, the properties of this set as a whole has not been much studied yet. Elementary questions are still open. Is it closed ? Connected ? What properties of G does it capture ? In this talk we will present some recent result regarding the growth spectrum of groups acting on a hyperbolic space, and illustrate with this example the diversity of techniques involved in this topic : geometry, combinatorics, probability theory, dynamical systems, etc.