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H 1 Amenable groups - Lecture 2

Auteurs : Bartholdi, Laurent (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : I shall discuss old and new results on amenability of groups, and more generally G-sets. This notion traces back to von Neumann in his study of the Hausdorff-Banach-Tarski paradox, and grew into one of the fundamental properties a group may / may not have -- each time with important consequences.
    Lecture 1. I will present the classical notions and equivalent definitions of amenability, with emphasis on group actions and on combinatorial aspects: Means, Folner sets, random walks, and paradoxical decompositions.
    Lecture 2. I will describe recent work by de la Salle et al. leading to a quite general criterion for amenability, as well as some still open problems. In particular, I will show that full topological groups of minimal Z-shifts are amenable.
    Lecture 3. I will explain links between amenability and cellular automata, in particular the "Garden of Eden" properties by Moore and Myhill: there is a characterization of amenable groups in terms of whether these classical theorems still hold.

    Codes MSC :
    37B10 - Symbolic dynamics
    37B15 - Cellular automata
    43A07 - Means on groups, semigroups, etc.; amenable groups
    68Q80 - Cellular automata (theory of computing)

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 08/12/16
      Date de captation : 30/11/16
      Collection : Research schools ; Combinatorics ; Computer Science ; Dynamical Systems and Ordinary Differential Equations
      Format : MP4
      Durée : 01:01:09
      Domaine : Combinatorics ; Computer Science ; Dynamical Systems & ODE
      Audience : Chercheurs ; Etudiants Science Cycle 2 ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2016-11-30_Bartholdi.mp4

    Informations sur la rencontre

    Nom de la rencontre : Combinatorics, automata and number theory / Combinatoire, automates et théorie des nombres
    Organisateurs de la rencontre : Berthé, Valérie ; Rigo, Michel
    Dates : 28/11/16 - 02/12/16
    Année de la rencontre : 2016
    URL Congrès : http://conferences.cirm-math.fr/1502.html

    Citation Data

    DOI : 10.24350/CIRM.V.19098603
    Cite this video as: Bartholdi, Laurent (2016). Amenable groups - Lecture 2. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19098603
    URI : http://dx.doi.org/10.24350/CIRM.V.19098603

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