En poursuivant votre navigation sur ce site, vous acceptez l'utilisation d'un simple cookie d'identification. Aucune autre exploitation n'est faite de ce cookie. OK
1

Mutually enriching connections between ergodic theory and combinatorics - part 4

Sélection Signaler une erreur
Multi angle
Auteurs : Bergelson, Vitaly (Auteur de la Conférence)
CIRM (Editeur )

Loading the player...

Résumé : * The early results of Ramsey theory :
Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres.

* Three main principles of Ramsey theory :
First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of this result. Third principle: The sought-after configurations which are always to be found in large sets are abundant.

* Furstenberg's Dynamical approach :
Partition Ramsey theory and topological dynamics Dynamical versions of van der Waerden's theorem, Hindman's theorem and Graham-Rothschild-Spencer's geometric Ramsey.
Density Ramsey theory and Furstenberg's correspondence principle Furstenberg's correspondence principle. Ergodic Szemeredi's theorem. Polynomial Szemeredi theorem. Density version of the Hales-Jewett theorem.

* Stone-Cech compactifications and Hindman's theorem :
Topological algebra in Stone-Cech compactifications. Proof of Hind-man's theorem via Poincare recurrence theorem for ultrafilters.

* IP sets and ergodic Ramsey theory :
Applications of IP sets and idempotent ultrafilters to ergodic-theoretical multiple recurrence and to density Ramsey theory. IP-polynomial Szemeredi theorem.

* Open problems and conjectures

If time permits:
* The nilpotent connection,
* Ergodic Ramsey theory and amenable groups

Codes MSC :
05D10 - Ramsey theory
11D41 - "Higher degree equations; Fermat's equation"
12D10 - Polynomials: location of zeros (algebraic theorems), {For the analytic theory, See 26C10, 30C15}
37Axx - Ergodic theory
37B20 - Notions of recurrence
54D80 - Special constructions of spaces (spaces of ultrafilters, etc.)

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 02/11/2016
    Date de captation : 18/10/2016
    Sous collection : Research School
    arXiv category : Dynamical Systems ; Combinatorics
    Domaine : Dynamical Systems & ODE ; Combinatorics
    Format : MP4 (.mp4) - HD
    Durée : 01:01:00
    Audience : Researchers
    Download : https://videos.cirm-math.fr/2016-10-18_Bergelson_4.mp4

Informations sur la Rencontre

Nom de la rencontre : Jean-Morlet Chair - Doctoral school: Applications of Ergodic Theory in Number Theory / Chaire Jean-Morlet - Ecole doctorale : Applications de la théorie ergodique à la théorie des nombres
Organisateurs de la rencontre : Adamczewski, Boris ; Ferenczi, Sébastien ; Kulaga-Przymus, Joanna ; Lemanczyk, Mariusz ; Troubetzkoy, Serge
Dates : 17/10/2016 - 21/10/2016
Année de la rencontre : 2016
URL Congrès : https://www.chairejeanmorlet.com/1560.html

Données de citation

DOI : 10.24350/CIRM.V.19072003
Citer cette vidéo: Bergelson, Vitaly (2016). Mutually enriching connections between ergodic theory and combinatorics - part 4. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19072003
URI : http://dx.doi.org/10.24350/CIRM.V.19072003

Voir aussi

Bibliographie



Sélection Signaler une erreur