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H 1 Representation theory, effective ergodic theorems, and applications - Lecture 3

Auteurs : Nevo, Amos (Auteur de la Conférence)
CIRM (Editeur )

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Résumé : Our first purpose is to show how aspects of the representation theory of (non-amenable) algebraic groups can be utilized to derive effective ergodic theorems for their actions. Our second purpose is to demonstrate some the many interesting applications that ergodic theorems with a rate of convergence have in a variety of problems. We will start by a discussion of property $T$ and show how to extend the spectral estimates it provides considerably beyond their usual formulations. We will also show how to derive best possible spectral estimates via representation theory in some cases. In turn, such spectral estimates will be used to derive effective ergodic theorems. Finally we will show how the rate of convergence in the ergodic theorem implies effective solutions in a host of natural problems, including the non-Euclidean lattice point counting problem, fast equidistribution of lattice orbits on homogenous spaces, and best possible exponents of Diophantine approximation on homogeneous algebraic varieties.

Codes MSC :
11F70 - Representation-theoretic methods; automorphic representations over local and global fields
37A15 - General groups of measure-preserving transformations
37A30 - Ergodic theorems, spectral theory, Markov operators
37P55 - Arithmetic dynamics on general algebraic varieties

 Informations sur la Vidéo Langue : Anglais Date de publication : 16/07/15 Date de captation : 01/07/15 Collection : Dynamical Systems and Ordinary Differential Equations ; Number Theory Sous collection : Research talks Format : quicktime ; audio/x-aac Domaine : Dynamical Systems & ODE ; Number Theory Durée : 01:00:17 Audience : Chercheurs ; Doctorants , Post - Doctorants Download : https://videos.cirm-math.fr/2015-07-01_Nevo_part3.mp4 Informations sur la rencontre Nom de la rencontre : Group representations in dynamical systems and geometry / Représentations des groupes en géométrie et dynamiqueOrganisateurs de la rencontre : Bufetov, Alexander ; Kuhn, Maria Gabriella ; Paoluzzi, Luisa ; Pavel, Nikitin ; Qiu, YanqiDates : 29/06/15 - 03/07/15 Année de la rencontre : 2015 URL Congrès : http://conferences.cirm-math.fr/1234.htmlCitation Data DOI : 10.24350/CIRM.V.18787203 Cite this video as: Nevo, Amos (2015). Representation theory, effective ergodic theorems, and applications - Lecture 3. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18787203 URI : http://dx.doi.org/10.24350/CIRM.V.18787203

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