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H 2 Random subgroups, totally non free actions and factor representations

Auteurs : Grigorchuk, Rostislav (Auteur de la Conférence)
CIRM (Editeur )

 Loading the player... Koopman representations totally non free actions groupoid representation factor representations example of totally non free action amenable groups just-infinite groups rooted trees branch groups symmetrized diagonal actions space of subgroups invariant random subgroups characteristic random subgroups groups of intermediate growth groups of geometric origin Questions hyperbolic groups and mapping class groups

Résumé : I will present results of three studies, performed in collaboration with M.Benli, L.Bowen, A.Dudko, R.Kravchenko and T.Nagnibeda, concerning the invariant and characteristic random subgroups in some groups of geometric origin, including hyperbolic groups, mapping class groups, groups of intermediate growth and branch groups. The role of totally non free actions will be emphasized. This will be used to explain why branch groups have infinitely many factor representations of type $II_1$.

Codes MSC :
20E08 - Groups acting on trees
20F65 - Geometric group theory
37B05 - Transformations and group actions with special properties (minimality, distality, proximality, etc.)

 Informations sur la Vidéo Langue : Anglais Date de publication : 15/07/15 Date de captation : 30/06/15 Collection : Research talks ; Algebra ; Dynamical Systems and Ordinary Differential Equations ; Geometry Format : QuickTime (.mov) Durée : 00:46:24 Domaine : Dynamical Systems & ODE ; Algebra ; Geometry Audience : Chercheurs ; Doctorants , Post - Doctorants Download : https://videos.cirm-math.fr/2015-06-30_Grigorchuk.mp4 Informations sur la rencontre Nom de la rencontre : Group representations in dynamical systems and geometry / Représentations des groupes en géométrie et dynamiqueOrganisateurs de la rencontre : Bufetov, Alexander ; Kuhn, Maria Gabriella ; Paoluzzi, Luisa ; Pavel, Nikitin ; Qiu, YanqiDates : 29/06/15 - 03/07/15 Année de la rencontre : 2015 URL Congrès : http://conferences.cirm-math.fr/1234.html Citation Data DOI : 10.24350/CIRM.V.18775603 Cite this video as: Grigorchuk, Rostislav (2015). Random subgroups, totally non free actions and factor representations. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18775603 URI : http://dx.doi.org/10.24350/CIRM.V.18775603

Bibliographie

• [1] Benli, M.G., Grigorchuk, R., & Nagnibeda, T. (2015). Universal groups of intermediate growth and their invariant random subgroups. - http://arxiv.org/abs/1503.01705

• [2] Bowen, L., Grigorchuk, R., & Kravchenko, R. (2013). Invariant random subgroups of the lamplighter group. - http://arxiv.org/abs/1206.6780

• [3] Bowen, L., Grigorchuk, R., & Kravchenko, R. (2015). Characteristic random subgroups of geometric groups and free abelian groups of infinite rank. - http://arxiv.org/abs/1402.3705

• [4] Dudko, A., & Grigorchuk, R. (2014). On diagonal actions of branch groups and the corresponding characters. - http://arxiv.org/abs/1412.5476

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