[{"command":"insert","method":null,"selector":".course-modal-ajax-placeholder-957880","data":"\u003Cdiv class=\u0022container content-rte\u0022\u003E\n \u003Cdiv class=\u0022row\u0022\u003E\n \u003Cdiv class=\u0022box col-md-6 bg-primary text-white\u0022\u003E\n \u003Ch2 class=\u0022h1 text-left\u0022\u003E Th\u00e9orie mesur\u00e9e des groupes 2025-2026\n\u003C\/h2\u003E\n \u003Cdiv class=\u0022field-spacing\u0022\u003E\n \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EECTS :\n 6\n \u003C\/div\u003E\n \u003C\/div\u003E\n \u003Cdiv class=\u0022field-spacing\u0022\u003E\n \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ESemestre calendaire :\n Semester 2\n \u003C\/div\u003E\n \u003C\/div\u003E\n \u003Cdiv class=\u0022field-spacing\u0022\u003E\n \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ED\u00e9tail du volume horaire\u003C\/div\u003E\n \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n \u003Cspan class=\u0022field__label h4 mt-5 \u0022\u003ECours magistraux :\u003C\/span\u003E\n \u003Cspan\u003E20\u003C\/span\u003E\n \u003C\/div\u003E\n \u003C\/div\u003E\n \u003Cdiv class=\u0022field-spacing\u0022\u003E\n \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ELangue d\u0026#039;enseignement\u003C\/div\u003E\n \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n \u003Cspan\u003EAnglais\u003C\/span\u003E\n \u003C\/div\u003E\n \u003C\/div\u003E\n \u003Cdiv class=\u0022field-spacing\u0022\u003E\n \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EEnseignement \u00e0 distance\u003C\/div\u003E\n \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n \u003Cspan\u003Enon\u003C\/span\u003E\n \u003C\/div\u003E\n \u003C\/div\u003E\n \u003C\/div\u003E\n \u003Cdiv class=\u0022box col-md-6\u0022\u003E\n \u003Cdiv class=\u0022field-spacing\u0022\u003E\n \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EProgramme \/ plan \/ contenus\u003C\/div\u003E\n \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n \u003Cspan\u003E\u003Cp\u003ELa th\u00e9orie mesur\u00e9e des groupes est une cousine de la th\u00e9orie g\u00e9om\u00e9trique des groupes : la premi\u00e8re \u00e9tudie les groupes \u00e0 travers leurs actions sur des espaces mesur\u00e9s, la seconde \u00e0 travers leurs actions sur des espaces m\u00e9triques. Le cours gravitera autour d\u0027une notion centrale en th\u00e9orie mesur\u00e9e des groupes, l\u0027\u00e9quivalence orbitale. Elle \u00e9tudie le probl\u00e8me suivant, qui trouve des motivations diverses allant de la g\u00e9om\u00e9trie aux alg\u00e8bres d\u0027op\u00e9rateurs : \u00e0 quelles conditions deux groupes peuvent-ils avoir des actions pr\u00e9servant la mesure sur un m\u00eame espace de probabilit\u00e9, avec les m\u00eames orbites ? Nous \u00e9tudierons ce probl\u00e8me en m\u00ealant des outils de nature ergodique et g\u00e9om\u00e9trique. Le cours sera organis\u00e9 comme suit. Nous commencerons par introduire les notions centrales (\u00e9quivalence orbitale et mesur\u00e9e) et leurs motivations. Nous mettrons ensuite en valeur plusieurs invariants d\u0027\u00e9quivalence orbitale (co\u00fbt, moyennabilit\u00e9,...), et \u00e9tudierons le probl\u00e8me de l\u0027\u00e9quivalence orbitale pour plusieurs familles importantes de groupes (groupes moyennables, groupes libres). Enfin, nous aborderons divers ph\u00e9nom\u00e8nes de rigidit\u00e9, fournissant des obstructions fortes \u00e0 ce que deux groupes puissent admettre de telles actions.\u003C\/p\u003E\n\u003Cp\u003EMeasured group theory is a cousin of geometric group theory: the former studies groups through their actions on measured spaces, the latter through their actions on metric spaces. The course will revolve around orbit equivalence, a central notion in measured group theory. It studies the following problem, which finds several motivations ranging from geometry to operator algebras: when can two groups act in a measure-preserving way on a probability space, with the same orbits? We will study this problem using both ergodic and geometric tools. The course will be organized as follows. We will first introduce the central notions (orbit and measure equivalence) and their motivations. We will highlight several invariants in orbit equivalence (cost, amenability,...), and study the orbit equivalence problem for several important families of groups (amenable groups, free groups). We will finally discuss several rigidity phenomena, giving strong obstructions for two groups to admit actions as above.\u003C\/p\u003E\u003C\/span\u003E\n \u003C\/div\u003E\n \u003C\/div\u003E\n \u003Cdiv class=\u0022field-spacing\u0022\u003E\n \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EBibliographie\u003C\/div\u003E\n \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n \u003Cspan\u003E\u003Cp\u003E[1] Alex Furman, A survey of measured group theory. In Geometry, rigidity, and group actions, 296-374. Chicago Lectures in Math. University of Chicago Press, Chicago IL, 2011. [2] Damien Gaboriau, Orbit equivalence and measured group theory. In Proceedings of the International Congress of Mathematicians. Volume III, 1501-1527. Hindustan Book Agency, New Delhi, 2010.\u003C\/p\u003E\u003C\/span\u003E\n \u003C\/div\u003E\n \u003C\/div\u003E\n \u003Cdiv class=\u0022field-spacing\u0022\u003E\n \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ENature de l\u0026#039;\u00e9valuation\u003C\/div\u003E\n \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n \u003Cspan\u003EEvaluation Terminale\u003C\/span\u003E\n \u003C\/div\u003E\n \u003C\/div\u003E\n \u003C\/div\u003E\n \u003C\/div\u003E\n\u003C\/div\u003E\n","settings":null}]