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Séminaire de théorie des groupes à l'ENS

Horaires : Le mardi 14 mai 2019, 14h--17h

Lieu : Salle W (DMA)

Après-midi de théorie de groupes

Stefan Witzel (Ecole Polytehchnique), Katie Vokes (IHES), Adrien Le Boudec (ENS Lyon)

14.00-14.45 Stefan Witzel (Ecole Polytehchnique) 15.00-15.45 Katie Vokes (IHES) 15.45-16.15 coffee break 16.15-16.45 Adrien Le Boudec (ENS Lyon) Stefan Witzel, Arithmetic approximate groups and their finiteness properties I 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 between arithmetic 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 surfaces In 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 model The goal of the talk will be to describe groups that are finitely generated, simple, and that act properly and cocompactly on the natural Cayley graph of the wreath product A wr F, where A is a finite group and F a non-abelian free group.

 

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