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Character rigidity and non-commutative ergodic theory

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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

    Langue : Anglais
    Date de publication : 23/10/2020
    Date de captation : 05/10/2020
    Sous collection : Research talks
    arXiv category : Dynamical Systems ; Group Theory ; Operator Algebras
    Domaine : Analysis and its Applications ; Dynamical Systems & ODE ; Lie Theory and Generalizations
    Format : MP4 (.mp4) - HD
    Durée : 00:47:52
    Audience : Researchers
    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

Données de citation

DOI : 10.24350/CIRM.V.19657403
Citer cette vidéo: 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

Bibliographie

  • 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

  • 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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