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