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H 1 Group actions on Lp spaces : dependence on p

Auteurs : de la Salle, Mikael (Auteur de la Conférence)
CIRM (Editeur )

Résumé : The study of group actions on Hilbert spaces is central in operator algebras, geometric group theory and representation theory. In many natural situations however, particularily interesting actions on Lp spaces appear for p not 2. One celebrated example is the construction by Pansu (and later greatly generalized by Yu to all Gromov hyperbolic groups) of proper actions of groups of isometries of hyperbolic spaces on Lp for large p. In all these results, the rather clear impression was that it was easier to act on Lp space as p becomes larger. The goal of my talk will be to explain this impression by a theorem and to study how the behaviour of the group actions on Lp spaces depends on p and on the group. In particular, I will show that the set of values of p such that a given countable groups has an isometric action on Lp with unbounded orbits is of the form $[p_c,\infty]$ for some $p_c$, and I will try to compute this critical parameter for lattices in semisimple groups. In passing, we will have to discuss how these objects and properties behave with respect to quantitative measure equivalence. This is a joint work with Amine Marrakchi, partly in arXiv:2001.02490.

Codes MSC :
22F05 - General theory of group and pseudogroup actions
46C05 - Hilbert and pre-Hilbert spaces: geometry and topology

 Informations sur la Vidéo Réalisateur : Hennenfent, Guillaume Langue : Anglais Date de publication : 23/10/2020 Date de captation : 07/10/2020 Collection : Research talks ; Analysis and its Applications Format : MP4 Durée : 00:48:22 Domaine : Analysis and its Applications Audience : Chercheurs ; Doctorants , Post - Doctorants Download : https://videos.cirm-math.fr/2020-10-07_De la Salle.mp4 Informations sur la rencontre Nom de la rencontre : Measured and Geometric Group Theory, Rigidity, Operator Algebras / Théorie mesurée et géométrique des groupes, rigidité, algèbres d’opérateursOrganisateurs de la rencontre : Gaboriau, Damien ; Houdayer, Cyril ; Szöke, Nóra Gabriella ; Tessera, RomainDates : 05/10/2020 - 10/10/2020 Année de la rencontre : 2020 URL Congrès : https://conferences.cirm-math.fr/2435.htmlCitation Data DOI : 10.24350/CIRM.V.19657503 Cite this video as: de la Salle, Mikael (2020). Group actions on Lp spaces : dependence on p. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19657503 URI : http://dx.doi.org/10.24350/CIRM.V.19657503

### Voir aussi

Bibliographie

1. MARRAKCHI, Amine et DE LA SALLE, Mikael. Isometric actions on Lp-spaces: dependence on the value of p. arXiv preprint arXiv:2001.02490, 2020. - https://arxiv.org/abs/2001.02490

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