# Geometria em Lisboa Seminar

### 07/05/2018, 16:30 — 17:30 — Room P3.10, Mathematics Building

Cyril Lecuire, *Centre National de la recherche scientifique*

### Geometry in groups

The intent of Geometric Group Theory is to deduce algebraic properties of groups from their actions on metric spaces. A natural way to obtain such an action is to equip a group with an invariant distance.

First, to motivate the study of Geometric Group Theory, I will expose some of its achievements (solvability of the word problem, Tits alternative). Then I will define the word metric on a finitely generated group and explain the difficulties raised by the definition. Finally, as an example of geometric properties of interest, I will introduce hyperbolic groups.