Après-midi de théorie de groupes

14.00-14.45 Stefan Witzel (Ecole Polytehchnique)15.00-15.45 Katie Vokes (IHES)15.45-16.15 coffee break16.15-16.45 Adrien Le Boudec (ENS Lyon)Stefan Witzel, Arithmetic approximate groups and their finiteness propertiesI will talk about approximate groups, a geometric generalization of groups. Approximate groups were discovered independently in various contexts and I will describe how they arise very naturally in the context of arithmetic groups. I will then explain how to extend topological finiteness properties of groups to approximate groups. This allows to make a connection betweenarithmetic groups in positive characteristic and arithmetic approximate groups in characteristic zero. The talk is based on joint work with Tobias Hartnick.Katie Vokes, Hierarchical hyperbolicity of graphs associated to surfacesIn a paper of 2000, Masur and Minsky studied the geometry of mapping class groups of surfaces using projections to certain Gromov hyperbolic graphs (the curve graphs) associated to subsurfaces. This inspired the definition by Behrstock, Hagen and Sisto of hierarchically hyperbolic spaces, which are equipped with similar projection maps, satisfying conditions which guarantee a structure analogous to that of the mapping class group. I will give some background on these concepts and present a result demonstrating that a large family of graphs associated to surfaces are hierarchically hyperbolic spaces.Adrien Le Boudec, Simple groups having a wreath product as a geometric modelThe goal of the talk will be to describe groups that are finitelygenerated, simple, and that act properly and cocompactly on thenatural Cayley graph of the wreath product A wr F, where A is afinite group and F a non-abelian free group.