** "Geometry and Analysis on Groups" Research Seminar **

**Time:** 2018.05.29, 15:00–17:00

**Location:** Seminarraum 10, Oskar-Morgenstern-Platz 1, 2.Stock

**Title:** "On the automorphism group of cyclic products of groups."

**Speaker:** Alexandre
Martin (Heriot-Watt University)

**Abstract:**
Graph products of groups are a construction that interpolates between direct products and free products, and contain well-known examples such as right-angled Coxeter groups and right-angled Artin groups. In this talk, I will present a form of rigidity for the automorphism group of ‘cyclic products of groups’, that is, the graph products over cycles on at least 5 vertices. I will recall a construction due to Davis that allows us to understand graph products through their action on CAT(0) cube complexes, and explain how this action extends to the whole automorphism group in the case of cyclic products of at least 5 groups. Such an action can be used to completely compute their automorphism group and to show their acylindrical hyperbolicity. This is joint work with Anthony Genevois.