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H 2 A universal hypercyclic representation

Auteurs : Glasner, Eli (Auteur de la Conférence)
CIRM (Editeur )

 Loading the player... ergodic dynamical systems Polish dynamical system general countable groups main theorem: universal linear system part 1: the Hilbert space and the representations part 2: the construction of the ergodic measure Grivaux's theorem Questions

Résumé : For any countable group, and also for any locally compact second countable, compactly generated topological group, $G$, there exists a "universal" hypercyclic representation on a Hilbert space, in the sense that it simultaneously models every possible ergodic probability measure preserving free action of $G$. I will discuss the original proof of this theorem (a joint work with Benjy Weiss) and then, at the end of the talk, say some words about the development of this idea and its applications as expounded in a subsequent work of Sophie Grivaux.

Codes MSC :
37A05 - Measure-preserving transformations
37A15 - General groups of measure-preserving transformations
37A25 - Ergodicity, mixing, rates of mixing
37A30 - Ergodic theorems, spectral theory, Markov operators
47A16 - Cyclic vectors, hypercyclic and chaotic operators
47A67 - Representation theory
47D03 - Groups and semigroups of linear operators

 Informations sur la Vidéo Langue : Anglais Date de publication : 03/11/15 Date de captation : 30/09/15 Collection : Research talks ; Analysis and its Applications ; Dynamical Systems and Ordinary Differential Equations Format : MP4 (.mp4) - HD Durée : 00:59:45 Domaine : Analysis and its Applications ; Dynamical Systems & ODE Audience : Chercheurs ; Doctorants , Post - Doctorants Download : https://videos.cirm-math.fr/2015-09-30_Glasner.mp4 Informations sur la rencontre Nom de la rencontre : Frontiers of operator dynamics / Frontières de la dynamique linéaireOrganisateurs de la rencontre : Grivaux, Sophie ; Lemanczyk, Marius ; Tomilov, YuriDates : 28/09/15 - 02/10/15 Année de la rencontre : 2015 URL Congrès : http://conferences.cirm-math.fr/1125.html Citation Data DOI : 10.24350/CIRM.V.18843403 Cite this video as: Glasner, Eli (2015). A universal hypercyclic representation. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18843403 URI : http://dx.doi.org/10.24350/CIRM.V.18843403

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