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H 1 Character rigidity and non-commutative ergodic theory

Auteurs : Boutonnet, Rémi (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : I will present a recent result in the theory of unitary representations of lattices in semi-simple Lie groups, which can be viewed as simultaneous generalization of Margulis normal subgroup theorem and C*-simplicity and the unique trace property for such lattices. The strategy of proof gathers ideas of both of these results: we extend Margulis’ dynamical approach to the non-commutative setting, and apply this to the conjugation dynamical system induced by a unitary representation. On the way, we obtain a new proof of Peterson’s character rigidity result, and a new rigidity result for uniformly recurrent subgroups of such lattices. I will give some basics on non-commutative ergodic theory and explain-some steps to prove the main result and its applications. This is based on joint works with Uri Bader, Cyril Houdayer, and Jesse Peterson.

    Keywords : characters; irreducible lattices; semi-simple Lie groups

    Codes MSC :
    22D10 - Unitary representations of locally compact groups
    22D25 - $C$*-algebras and $W$*-algebras arising from group representations, See also {46Lxx}
    22E40 - Discrete subgroups of Lie groups
    46L10 - General theory of von Neumann algebras
    46L30 - States

    Ressources complémentaires :
    https://www.cirm-math.fr/RepOrga/2435/Notes/Notes-Boutonnet-cirm.pdf

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 23/10/2020
      Date de captation : 05/10/2020
      Collection : Research talks ; Analysis and its Applications ; Dynamical Systems and Ordinary Differential Equations ; Lie Theory and Generalizations
      Format : MP4
      Durée : 00:47:52
      Domaine : Analysis and its Applications ; Dynamical Systems & ODE ; Lie Theory and Generalizations
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2020-10-05_Boutonnet.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.19657403
    Cite this video as: Boutonnet, Rémi (2020). Character rigidity and non-commutative ergodic theory. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19657403
    URI : http://dx.doi.org/10.24350/CIRM.V.19657403


    Voir aussi

    Bibliographie

    1. BOUTONNET, Rémi et HOUDAYER, Cyril. Stationary characters on lattices of semisimple Lie groups. arXiv preprint arXiv:1908.07812, 2019. - https://arxiv.org/abs/1908.07812

    2. BADER, Uri, BOUTONNET, Rémi, HOUDAYER, Cyril, et al. Charmenability of arithmetic groups of product type. arXiv preprint arXiv:2009.09952, 2020. - https://arxiv.org/abs/2009.09952

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