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V

- 253 p.
ISBN 978-3-7643-8411-1

Trends in mathematics

Localisation : Colloque RdC (GENE)

théorie des groupes # groupes géométriques # algèbre de groupe localement compact

20-06 ; 20F65 ; 00B25 ; 20-XX ; 22Dxx

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Research schools

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.
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: ...

37B15 ; 37B10 ; 43A07 ; 68Q80

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V

- 413 p.
ISBN 978-3-7643-7446-4

Progress in mathematics , 0248

Localisation : Collection 1er étage

groupe infini # théorie ergodique # algèbre d'opérateur autoadjoint # limite # groupe profini # méthode probabiliste # groupe amenable # groupe de Khäler # rigidité # c*algèbre # groupe automorphique # marche aléatoire # groupe de Burnside # groupe Fuchsien

20Fxx ; 37Axx ; 46Lxx ; 20E18 ; 20P05 ; 43A07 ; 55R35

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