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.