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

**Time:** 2015.12.15, 15:00–17:00

**Location:** Seminarraum 8, Oskar-Morgenstern-Platz 1, 2.Stock

**Title:** "Acylindrical hyperbolicity of diagram groups from
cubical geometry."

**Speaker:** Anthony Genevois (Aix-Marseille Université)

**Abstract:**
The first part of the talk will be essentially dedicated to the
introduction of the diagram groups and the CAT(0) cube complexes on which
they act. Afterwards, the problem we will be interested in is to use this
action in order to study some negatively-curved properties of diagram
groups, in particular their acylindrical hyperbolicity. Thanks to a
general construction due to Bestvina, Bromberg and Fujiwara, a sufficient
condition to deduce the acylindrical hyperbolicity of a diagram group is
to find contracting isometries in the action on its associated cube
complex. The goal of the second part of the talk will be to introduce a
characterization of contracting isometries of a CAT(0) cube complex, and
then to show how it may be applied to diagram groups, giving a simple
method to determine precisely when an element of the group induces or not
a contracting isometry of its cube complex.