{"id":420,"date":"2022-01-18T11:23:59","date_gmt":"2022-01-18T10:23:59","guid":{"rendered":"https:\/\/imag.umontpellier.fr\/wordpress\/?page_id=420"},"modified":"2026-03-02T09:00:46","modified_gmt":"2026-03-02T08:00:46","slug":"gta","status":"publish","type":"page","link":"https:\/\/imag.umontpellier.fr\/?page_id=420","title":{"rendered":"GTA"},"content":{"rendered":"\n<h2 class=\"wp-block-heading is-style-default\" id=\"geometrie-topologie-et-algebre\"><strong>G\u00e9om\u00e9trie, Topologie et Alg\u00e8bre<\/strong><\/h2>\n\n\n\n<div class=\"wp-block-group is-layout-flow wp-block-group-is-layout-flow\">\n<p>Responsable : <a href=\"https:\/\/imag.umontpellier.fr\/?page_id=524&amp;id=31\">Damien CALAQUE<\/a><br>Gestionnaire : <a href=\"https:\/\/imag.umontpellier.fr\/?page_id=524&amp;id=104\">Carmela MADONIA<\/a><\/p>\n\n\n\n<p><a href=\"https:\/\/imag.umontpellier.fr\/?page_id=13&amp;eqp=GTA\">Composition de l&rsquo;\u00e9quipe<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"themes-de-recherche\"><strong>Th\u00e8mes de recherche :<\/strong><\/h2>\n<\/div>\n\n\n\n<div class=\"wp-block-group is-layout-flow wp-block-group-is-layout-flow\">\n<p>L\u2019\u00e9quipe GTA couvre un large champ des math\u00e9matiques fondamentales, comprenant la g\u00e9om\u00e9trie (alg\u00e9brique, diff\u00e9rentielle, non commutative, discr\u00e8te et convexe), la topologie (alg\u00e9brique ou diff\u00e9rentielle) et l\u2019alg\u00e8bre au sens large (combinatoire alg\u00e9brique, th\u00e9orie des groupes, th\u00e9orie des nombres, repr\u00e9sentations, alg\u00e8bre homologique et homotopique). Elle est principalement structur\u00e9e par deux s\u00e9minaires hebdomadaires\u00a0: AGATA et Darboux.<\/p>\n<\/div>\n\n\n\n<p><strong><em>AGATA :<\/em><\/strong><\/p>\n\n\n\n<div class=\"wp-block-group is-layout-flow wp-block-group-is-layout-flow\">\n<p>Le s\u00e9minaire AGATA (Arithm\u00e9tique, G\u00e9om\u00e9trie Alg\u00e9brique, Topologie Alg\u00e9brique) accueille les th\u00e9matiques les plus port\u00e9es vers l\u2019alg\u00e8bre de l\u2019\u00e9quipe. Un d\u00e9nominateur commun \u00e0 une majorit\u00e9 de participant.es du s\u00e9minaire est la notion de repr\u00e9sentation et l\u2019utilisation d\u2019outils de nature (co)homologique.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong><em>Alg\u00e8bre et g\u00e9om\u00e9trie combinatoires\u00a0: <\/em><\/strong>matro\u00efdes, polyn\u00f4me d\u2019Ehrhart, empilements Apolloniens, ombres de diagrammes d\u00e9nou\u00e9s et d\u2019entrelacs positifs, repr\u00e9sentation avec des boules, op\u00e9rades, polytopes, posets.<\/li>\n\n\n\n<li><strong><em>Topologie, alg\u00e8bre quantique\u00a0et g\u00e9om\u00e9trie non commutative : <\/em><\/strong>TQFT, invariants de noeuds et de 3-vari\u00e9t\u00e9s, invariants quantiques hyperboliques, vari\u00e9t\u00e9s de caract\u00e8res et leurs quantifications, cat\u00e9gorification, homologie de Hochschild, K-th\u00e9orie.<\/li>\n\n\n\n<li><strong><em>G\u00e9om\u00e9trie alg\u00e9brique et arithm\u00e9tique\u00a0: <\/em><\/strong>motifs et p\u00e9riodes, espaces de modules, champs alg\u00e9briques, g\u00e9om\u00e9trie d\u00e9riv\u00e9e, g\u00e9om\u00e9trie birationnelle, K-stabilit\u00e9.<\/li>\n\n\n\n<li><strong><em>Repr\u00e9sentations\u00a0: <\/em><\/strong>groupes alg\u00e9briques\/de Lie, groupes quantiques, th\u00e9orie g\u00e9om\u00e9trique des repr\u00e9sentations, m\u00e9thode des orbites et quantification g\u00e9om\u00e9trique, produits tensoriels, groupes de r\u00e9flexions, vari\u00e9t\u00e9s sph\u00e9riques\/de drapeaux, programme de Langlands.<\/li>\n<\/ul>\n<\/div>\n\n\n\n<p><em><strong>DARBOUX :<\/strong><\/em><\/p>\n\n\n\n<div class=\"wp-block-group is-layout-flow wp-block-group-is-layout-flow\">\n<p>Le s\u00e9minaire Gaston Darboux accueille les th\u00e9matiques les plus port\u00e9es vers les m\u00e9thodes analytiques et m\u00e9triques dans l\u2019\u00e9quipe. Un d\u00e9nominateur commun \u00e0 une majorit\u00e9 de participant.es du s\u00e9minaire est la notion de courbure.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong><em>Th\u00e9orie g\u00e9om\u00e9trique des groupes<\/em><\/strong><strong><em>\u00a0: <\/em><\/strong>g\u00e9om\u00e9trie hyperbolique, g\u00e9om\u00e9trie des groupes discrets, courbure n\u00e9gative, tresses.<\/li>\n\n\n\n<li><strong><em>G\u00e9om\u00e9trie diff\u00e9rentielle et analyse globale\u00a0:<\/em><\/strong> g\u00e9om\u00e9trie asymptotique, g\u00e9om\u00e9trie conforme, structures g\u00e9om\u00e9triques, th\u00e9orie spectrale, in\u00e9galit\u00e9s isop\u00e9rim\u00e9triques, prescription de courbure, vari\u00e9t\u00e9s pseudo-riemanniennes, th\u00e9orie de Teichm\u00fcller, 3-vari\u00e9t\u00e9s, g\u00e9om\u00e9trie des convexes, m\u00e9triques K\u00e4hleriennes, op\u00e9rateurs de Dirac et th\u00e9orie de l\u2019indice.<\/li>\n\n\n\n<li><strong><em>Dynamique et th\u00e9orie ergodique<\/em><\/strong>\u00a0: marches al\u00e9atoires sur les groupes, dynamique des espaces homog\u00e8nes, flots en courbure n\u00e9gative, surfaces de translation, entropie volumique.<\/li>\n<\/ul>\n\n\n\n<p>L\u2019\u00e9tude des surfaces, de leurs groupes modulaires, et des repr\u00e9sentations de ceux-ci, transcende n\u00e9anmoins cette structuration bic\u00e9phale. En effet, l\u2019\u00e9quipe GTA pourrait en partie reprendre \u00e0 son compte cette conclusion de l\u2019<em>Esquisse d\u2019un programme<\/em> d\u2019Alexandre Grothendieck<a href=\"#_ftn1\" id=\"_ftnref1\">[1]<\/a>&nbsp;:<\/p>\n\n\n\n<p><em>\u00ab&nbsp;Derri\u00e8re la disparit\u00e9 apparente des th\u00e8mes \u00e9voqu\u00e9s ici, un lecteur attentif percevra comme moi une unit\u00e9 profonde. Celle-ci se manifeste notamment par une source d\u2019inspiration commune, la g\u00e9om\u00e9trie des surfaces, pr\u00e9sente dans tous ces th\u00e8mes, au premier plan le plus souvent.&nbsp;\u00bb<\/em><em><\/em><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><a href=\"#_ftnref1\" id=\"_ftn1\">[1]<\/a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <a href=\"https:\/\/grothendieck.umontpellier.fr\/archives-grothendieck\/\">Archives Grothendieck<\/a>, cote 119, page 53.<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>G\u00e9om\u00e9trie, Topologie et Alg\u00e8bre Responsable : Damien CALAQUEGestionnaire : Carmela MADONIA Composition de l&rsquo;\u00e9quipe Th\u00e8mes de recherche : L\u2019\u00e9quipe GTA couvre un large champ des [&#8230;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":398,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-420","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/imag.umontpellier.fr\/index.php?rest_route=\/wp\/v2\/pages\/420","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/imag.umontpellier.fr\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/imag.umontpellier.fr\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/imag.umontpellier.fr\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/imag.umontpellier.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=420"}],"version-history":[{"count":16,"href":"https:\/\/imag.umontpellier.fr\/index.php?rest_route=\/wp\/v2\/pages\/420\/revisions"}],"predecessor-version":[{"id":2557,"href":"https:\/\/imag.umontpellier.fr\/index.php?rest_route=\/wp\/v2\/pages\/420\/revisions\/2557"}],"up":[{"embeddable":true,"href":"https:\/\/imag.umontpellier.fr\/index.php?rest_route=\/wp\/v2\/pages\/398"}],"wp:attachment":[{"href":"https:\/\/imag.umontpellier.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=420"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}