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Documents  22F05 | enregistrements trouvés : 6

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- x; 163 p.
ISBN 978-0-8218-6872-0

Contemporary mathematics , 0549

Localisation : Collection 1er étage

symétrie # équation différentielle # équation algébrique différentielle

35A30 ; 34M15 ; 17B45 ; 35C05 ; 70A05 ; 37J05 ; 22F05 ; 53A04 ; 39A13 ; 35-06 ; 00B25

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The study of group actions on Hilbert spaces is central in operator algebras, geometric group theory and representation theory. In many natural situations however, particularily interesting actions on Lp spaces appear for p not 2. One celebrated example is the construction by Pansu (and later greatly generalized by Yu to all Gromov hyperbolic groups) of proper actions of groups of isometries of hyperbolic spaces on Lp for large p. In all these results, the rather clear impression was that it was easier to act on Lp space as p becomes larger. The goal of my talk will be to explain this impression by a theorem and to study how the behaviour of the group actions on Lp spaces depends on p and on the group. In particular, I will show that the set of values of p such that a given countable groups has an isometric action on Lp with unbounded orbits is of the form $[p_c,\infty]$ for some $p_c$, and I will try to compute this critical parameter for lattices in semisimple groups. In passing, we will have to discuss how these objects and properties behave with respect to quantitative measure equivalence. This is a joint work with Amine Marrakchi, partly in arXiv:2001.02490. The study of group actions on Hilbert spaces is central in operator algebras, geometric group theory and representation theory. In many natural situations however, particularily interesting actions on Lp spaces appear for p not 2. One celebrated example is the construction by Pansu (and later greatly generalized by Yu to all Gromov hyperbolic groups) of proper actions of groups of isometries of hyperbolic spaces on Lp for large p. In all these ...

22F05 ; 46C05

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Algebra;Dynamical Systems and Ordinary Differential Equations

A subgroup of a group is confined if the closure of its conjugacy class in the Chabauty space does not contain the trivial subgroup. Such subgroups arise naturally as stabilisers for non-free actions on compact spaces. I will explain a result establishing a relation between the confined subgroup of a group with its highly transitive actions. We will see how this result allows to understand the highly transitive actions of a class of groups of dynamical origin. This is joint work with Adrien Le Boudec. A subgroup of a group is confined if the closure of its conjugacy class in the Chabauty space does not contain the trivial subgroup. Such subgroups arise naturally as stabilisers for non-free actions on compact spaces. I will explain a result establishing a relation between the confined subgroup of a group with its highly transitive actions. We will see how this result allows to understand the highly transitive actions of a class of groups of ...

20B22 ; 37B05 ; 22F05

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- 302 p.
ISBN 978-3-03719-016-6

EMS textbooks in mathematics

Localisation : Ouvrage RdC (STRO)

groupe localement compacts # groupe fini # représentation de groupe # groupe automorphe # semi-groupe topologique # intégrale de Haar # théorème de Peter-Weyl # problème de Hilbert # transformation de groupe # structure de semi-groupe topologique

22D05 ; 22-01 ; 20E18 ; 22A25 ; 22C05 ; 22D10 ; 22D45 ; 22F05 ; 12J10 ; 43A05 ; 54H15 ; 22A15

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- 192 p.
ISBN 978-0-8218-4137-2

University lecture series , 0040

Localisation : Collection 1er étage

combinatoires # groupe topologique # théorie de Ramsey # théorie des groupes # mesure sur les groupes # méthode probaliste # espace de Banach # groupe de dimension infinie # phénomène de Ramsey-Dvoretzky-Milman # groupe de Lévy

05-02 ; 22-02 ; 05D10 ; 22F05 ; 43A05 ; 46B09

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- ix, 140 p.
ISBN 978-0-8218-4711-4

Memoirs of the american mathematical society , 0968

Localisation : Collection 1er étage

théorie de Ramsey # espace métrique # groupe topologique # géométrie métrique # théorie de Fraïsé # actions de groupes topologiques # flot minimal universel

03E02 ; 05C55 ; 05D10 ; 22A05 ; 22F05 ; 51F99

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