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H 1 Character rigidity and non-commutative ergodic theory

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

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’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.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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