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Laurent Bartholdi Amenable groups Lecture 2
>> YOUR LINK HERE: ___ http://youtube.com/watch?v=uNhTH6FUiuo
Abstract: 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. • Recording during the thematic meeting : CANT 2016 (Combinatoire, Automates et Théorie des Nombres) the November 30, 2016 at the Centre International de Rencontres Mathématiques (Marseille, France) • Filmmaker: Guillaume Hennenfent • Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: • Chapter markers and keywords to watch the parts of your choice in the video • Videos enriched with abstracts, bibliographies, Mathematics Subject Classification • Multi-criteria search by author, title, tags, mathematical area
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