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

Collection Measured and Geometric Group Theory, Rigidity, Operator Algebras / Théorie mesurée et géométrique des groupes, rigidité, algèbres d’opérateurs

Organizer(s) Gaboriau, Damien ; Houdayer, Cyril ; Szöke, Nóra Gabriella ; Tessera, Romain

Date(s) 05/10/2020 - 10/10/2020

linked URL https://conferences.cirm-math.fr/2435.html

00:00:00 / 00:00:00

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Character rigidity and non-commutative ergodic theory

By Rémi Boutonnet

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.

Information about the video

Date of recording 05/10/2020
Date of publication 23/10/2020
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19657403
Cite this video 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

Domain(s)

Bibliography

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

MSC codes

Document(s)

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

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