{"id":282,"date":"2024-11-27T15:46:05","date_gmt":"2024-11-27T14:46:05","guid":{"rendered":"https:\/\/www.imj-prg.fr\/tga\/?p=282"},"modified":"2025-06-17T17:07:25","modified_gmt":"2025-06-17T15:07:25","slug":"demi-journee-dequipe-9-decembre-2024","status":"publish","type":"post","link":"https:\/\/www.imj-prg.fr\/tga\/demi-journee-dequipe-9-decembre-2024\/","title":{"rendered":"Demi-journ\u00e9e d&rsquo;\u00e9quipe &#8211; 9 d\u00e9cembre 2024"},"content":{"rendered":"\n<p>La prochaine (demi-)journ\u00e9e de l&rsquo;\u00e9quipe TGA aura lieu le lundi 9 d\u00e9cembre prochain, de 14h \u00e0 18h \u00e0 Jussieu (salle 1525-502).<\/p>\n\n\n\n<p>Elle consistera en une s\u00e9rie d&rsquo;expos\u00e9s de nouveaux membres de l&rsquo;\u00e9quipe (Yonatan Harpaz, Mirko Mauri, Enrica Mazzon, Manh Linh Nguyen, et Victor Roca Lucio), et sera suivie d&rsquo;un ap\u00e9ritif d\u00eenatoire.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Yonatan Harpaz (14h-14h30) : Homotopy symmetric hermitian K-theory<br><\/strong>Hermitian K-theory is a type of cohomology theory on rings and schemes similar to algebraic K-theory, where instead of projective modules one takes quadratic forms. The latter are considerably more tractable when working over base rings in which $2$ is invertible. For example, under this assumption the work of Hornbostel and Schlichting shows that hermitian K-theory satisfies A^1-invariance, devissage and purity over regular Noetherian schemes, properties which do not hold in general when 2 is not invertible. In this talk I will present joint work with Baptiste Calm\u00e8s and Denis Nardin showing that, for regular Noetherian schemes of finite Krull dimension, one can recover this excellent behavior without assuming 2 is invertible if instead of quadratic or symmetric bilinear forms one considers \u00ab\u00a0homotopy symmetric\u00a0\u00bb forms. In addition, we also show that under this hypothesis classical and homotopy symmetric hermitian K-theory agree in sufficiently high degrees, thus recovering \u00ab\u00a0eventual\u00a0\u00bb $A^1$-invariance for classical hermitian K-theory.<\/li>\n\n\n\n<li><strong>Mirko Mauri (14h45-15h15) : Decomposition theorem for Lagrangian fibrations<\/strong><br>Moduli spaces of sheaves on K3 or abelian surfaces or moduli spaces of $G$-Higgs bundles are prototypes of holomorphic symplectic varieties endowed with a Lagrangian fibration, called Beauville\u2013Mukai or Hitchin system respectively. The decomposition theorem informs us about symmetries of the cohomology of these moduli spaces like Euler characteristic independence or topological mirror symmetry.The talk is based on a joint work with Migliorini and Pagaria, and ongoing projects with de Cataldo, Fringuelli and Herrero, and with Kim and Sawon.<\/li>\n\n\n\n<li>Pause caf\u00e9<\/li>\n\n\n\n<li><strong>Enrica Mazzon (16h-16h30) : Higher Fano Manifolds<\/strong><br>Fano manifolds are complex projective manifolds characterized by a positive first Chern class. This positivity condition has profound geometric and arithmetic consequences. For example, Fano manifolds are covered by rational curves, and families of Fano manifolds over one-dimensional bases always admit holomorphic sections.<br>Recently, there has been significant interest in defining suitable higher analogues of the Fano condition. Higher Fano manifolds are conjectured to exhibit stronger versions of the remarkable properties of Fano manifolds. In this talk, I will introduce a potential notion of higher Fano manifolds based on the positivity of higher Chern characters and explore the special geometric features that distinguish these manifolds.<\/li>\n\n\n\n<li><strong>Manh-Linh Nguyen (16h45-17h15) : L&rsquo;obstruction de Brauer\u2013Manin et la m\u00e9thode de la descente<\/strong><br>Soit $X$ une vari\u00e9t\u00e9 alg\u00e9brique d\u00e9finie sur un corps de nombres $k$. Une question fondamentale en g\u00e9om\u00e9trie arithm\u00e9tique est de d\u00e9cider si $X$ poss\u00e8de un point $k$-rationnel. Une condition n\u00e9cessaire \u00e9vidente est que $X$ ait des points locaux dans tous les compl\u00e9t\u00e9s $k_v$ de $k$, mais cela n&rsquo;est pas toujours suffisant (dans ce cas, on dit que $X$ est un contre-exemple au principe de Hasse). Nous introduisons dans cet expos\u00e9 une obstruction cohomologique d\u00e9finie par Manin permettant de d\u00e9tecter le d\u00e9faut du principe de Hasse, ainsi qu&rsquo;une propri\u00e9t\u00e9 appel\u00e9e \u00ab approximation faible \u00bb. Nous pr\u00e9sentons ensuite la th\u00e9orie de la descente, une m\u00e9thode due \u00e0 Colliot-Th\u00e9l\u00e8ne et Sansuc. L&rsquo;esprit de cette derni\u00e8re est englob\u00e9 dans une \u00ab conjecture de descente \u00bb, qui a \u00e9t\u00e9 r\u00e9cemment formul\u00e9e par Wittenberg. Nous discuterons les cas connus de cette conjecture-l\u00e0, \u00e0 savoir ceux des torseurs sous un tore, un groupe fini hyper-r\u00e9soluble (Harpaz\u2013Wittenberg, 2020 et 2022) ou un groupe lin\u00e9aire connexe (L., 2023).<\/li>\n\n\n\n<li><strong>Victor Roca i Lucio (17h30-18h) : Th\u00e9orie de Lie sup\u00e9rieure en caract\u00e9ristique positive<\/strong><br>\u00c9tant donn\u00e9 une alg\u00e8bre de Lie nilpotente sur un corps de caract\u00e9ristique nulle, on peut construire un groupe de fa\u00e7on universelle via la formule de Baker-Campbell-Hausdorff. Cette proc\u00e9dure d&rsquo;int\u00e9gration admet des g\u00e9n\u00e9ralisations homotopiques pour les alg\u00e8bres de Lie differentielles gradu\u00e9es ainsi que pour les alg\u00e8bres de Lie \u00e0 homotopie pr\u00e8s; dans ces cas l\u00e0 nous obtenons non plus un groupe, mais un infini groupo\u00efde. Celui-ci s&rsquo;interpr\u00e8te comme l&rsquo;infini groupo\u00efde des d\u00e9formations infinit\u00e9simales qu&rsquo;encode l&rsquo;alg\u00e8bre de Lie diff\u00e9rentielle gradu\u00e9e sous la correspondance de Lurie-Pridham. Gr\u00e2ce aux r\u00e9cents travaux de Brantner-Mathew, cette correspondance entre probl\u00e8mes de d\u00e9formation infinit\u00e9simaux et les structures alg\u00e9briques de type Lie a \u00e9t\u00e9 \u00e9tendue en caract\u00e9ristique positive, avec de l&rsquo;autre c\u00f4t\u00e9 ce qu&rsquo;on appelle les alg\u00e8bres de Lie \u00e0 partitions. Dans cet expos\u00e9, je construirai un analogue du foncteur d&rsquo;int\u00e9gration pour ces alg\u00e8bres de Lie \u00e0 partitions. J&rsquo;expliquerai comment relier ces constructions \u00e0 celles qui existent en caract\u00e9ristique nulle. Finalement, je parlerai de quelques applications en th\u00e9orie de l&rsquo;homotopie $p$-adique.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>La prochaine (demi-)journ\u00e9e de l&rsquo;\u00e9quipe TGA aura lieu le lundi 9 d\u00e9cembre prochain, de 14h \u00e0 18h \u00e0 Jussieu (salle 1525-502). Elle consistera en une s\u00e9rie d&rsquo;expos\u00e9s de nouveaux membres de l&rsquo;\u00e9quipe (Yonatan Harpaz, Mirko Mauri, Enrica Mazzon, Manh Linh Nguyen, et Victor Roca Lucio), et sera suivie d&rsquo;un ap\u00e9ritif d\u00eenatoire.<\/p>\n","protected":false},"author":41,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-282","post","type-post","status-publish","format-standard","hentry","category-non-classe"],"_links":{"self":[{"href":"https:\/\/www.imj-prg.fr\/tga\/wp-json\/wp\/v2\/posts\/282","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.imj-prg.fr\/tga\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.imj-prg.fr\/tga\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.imj-prg.fr\/tga\/wp-json\/wp\/v2\/users\/41"}],"replies":[{"embeddable":true,"href":"https:\/\/www.imj-prg.fr\/tga\/wp-json\/wp\/v2\/comments?post=282"}],"version-history":[{"count":15,"href":"https:\/\/www.imj-prg.fr\/tga\/wp-json\/wp\/v2\/posts\/282\/revisions"}],"predecessor-version":[{"id":317,"href":"https:\/\/www.imj-prg.fr\/tga\/wp-json\/wp\/v2\/posts\/282\/revisions\/317"}],"wp:attachment":[{"href":"https:\/\/www.imj-prg.fr\/tga\/wp-json\/wp\/v2\/media?parent=282"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.imj-prg.fr\/tga\/wp-json\/wp\/v2\/categories?post=282"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.imj-prg.fr\/tga\/wp-json\/wp\/v2\/tags?post=282"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}