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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 )

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    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

      Langue : Anglais
      Date de publication : 23/10/2020
      Date de captation : 07/10/2020
      Sous collection : Research talks
      Format : MP4
      arXiv category : Group Theory ; Functional Analysis
      Domaine : Analysis and its Applications
      Durée : 00:48:22
      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’opérateurs
    Organisateurs de la rencontre : Gaboriau, Damien ; Houdayer, Cyril ; Szöke, Nóra Gabriella ; Tessera, Romain
    Dates : 05/10/2020 - 10/10/2020
    Année de la rencontre : 2020
    URL Congrès : https://conferences.cirm-math.fr/2435.html

    Citation 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


    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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