Character rigidity and non-commutative ergodic theory | Vidéo | Carmin.tv

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Character rigidity and non-commutative ergodic theory

De Rémi Boutonnet

Apparaît dans la collection : Measured and Geometric Group Theory, Rigidity, Operator Algebras / Théorie mesurée et géométrique des groupes, rigidité, algèbres d’opérateurs

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 C²-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.

Informations sur la vidéo

Date de captation 05/10/2020
Date de publication 23/10/2020
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19657403
Citer cette vidéo Boutonnet, Rémi (05/10/2020). Character rigidity and non-commutative ergodic theory. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19657403
URL https://dx.doi.org/10.24350/CIRM.V.19657403

Domaine(s)

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

Codes MSC

Document(s)

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

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