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A universal hypercyclic representation
Post-edited
Authors : Glasner, Eli (Author of the conference)
CIRM (Publisher )
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
CIRM (Publisher )
Abstract :
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.
MSC Codes : 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
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 03/11/15 Conference Date : 30/09/15 Subseries : Research talks arXiv category : Dynamical Systems ; Functional Analysis Mathematical Area(s) : Analysis and its Applications ; Dynamical Systems & ODE Format : MP4 (.mp4) - HD Video Time : 00:59:45 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2015-09-30_Glasner.mp4 
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Information on the Event
Event Title : Frontiers of operator dynamics / Frontières de la dynamique linéaireEvent Organizers : Grivaux, Sophie ; Lemanczyk, Marius ; Tomilov, Yuri Dates : 28/09/15 - 02/10/15 Event Year : 2015 Event URL : http://conferences.cirm-math.fr/1125.html
Citation Data
DOI : 10.24350/CIRM.V.18843403Cite 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 |
Bibliography
- Glasner, E., & Weiss, B. (2015). A universal hypercyclic representation. Journal of Functional Analysis, 268(11), 3478-3491 - http://dx.doi.org/10.1016/j.jfa.2015.02.002
