{"id":431,"date":"2021-04-08T10:53:45","date_gmt":"2021-04-08T20:53:45","guid":{"rendered":"https:\/\/recherche.upf.pf\/?post_type=laboratoire&#038;p=431"},"modified":"2025-10-15T08:41:51","modified_gmt":"2025-10-15T18:41:51","slug":"gaati","status":"publish","type":"laboratoire","link":"https:\/\/recherche.upf.pf\/ty\/laboratoire\/gaati\/","title":{"rendered":"GAATI \u2014 G\u00e9om\u00e9trie Alg\u00e9brique et Applications \u00e0 la Th\u00e9orie de l\u2019Information"},"content":{"rendered":"<p class=\"qtranxs-available-languages-message qtranxs-available-languages-message-ty\">D\u00e9sol\u00e9, ce contenu est uniquement disponible en <a href=\"https:\/\/recherche.upf.pf\/fr\/wp-json\/wp\/v2\/laboratoire\/431\" class=\"qtranxs-available-language-link qtranxs-available-language-link-fr\" title=\"Fran\u00e7ais\">Fran\u00e7ais<\/a> et <a href=\"https:\/\/recherche.upf.pf\/en\/wp-json\/wp\/v2\/laboratoire\/431\" class=\"qtranxs-available-language-link qtranxs-available-language-link-en\" title=\"English\">English<\/a>.<\/p><p>Le laboratoire de G\u00e9om\u00e9trie Alg\u00e9brique et Applications \u00e0 la Th\u00e9orie de l&#8217;Information (GAATI) est une unit\u00e9 de recherche en math\u00e9matiques accr\u00e9dit\u00e9e depuis 2004 par le minist\u00e8re de l&#8217;enseignement sup\u00e9rieur et de la recherche (EA 3893). C&#8217;est l&#8217;unique structure de recherche en math\u00e9matiques en Polyn\u00e9sie fran\u00e7aise.<\/p>\n<p>Les travaux du laboratoire GAATI visent \u00e0 am\u00e9liorer l&#8217;efficacit\u00e9 et la s\u00e9curit\u00e9 des syst\u00e8mes de transport et de contr\u00f4le de l&#8217;information par le d\u00e9veloppement de nouvelles techniques algorithmiques et cryptographiques. Pour cela, le laboratoire d\u00e9veloppe et exploite des m\u00e9thodes math\u00e9matiques bas\u00e9es sur la g\u00e9om\u00e9trie alg\u00e9brique et la th\u00e9orie des nombres.<\/p>\n<p>Les principaux th\u00e8mes de recherche du laboratoire GAATI sont&nbsp;:<\/p>\n<ul>\n<li>Les aspects algorithmiques des courbes alg\u00e9briques et des vari\u00e9t\u00e9s ab\u00e9liennes&nbsp;: calcul efficace de la loi de groupe&nbsp;; nombre de points et logarithme discret des vari\u00e9t\u00e9s sur les corps finis&nbsp;; aspects effectifs de la th\u00e9orie de la multiplication complexe&nbsp;; calcul d\u2019anneaux des  endomorphismes&nbsp;; constructions explicites de vari\u00e9t\u00e9s&nbsp;; applications en cryptographie.<\/li>\n<li>Les fonctions bool\u00e9ennes de faible uniformit\u00e9 diff\u00e9rentielle&nbsp;: fonctions APN et la conjecture APN&nbsp;; construction de fonctions de faible uniformit\u00e9 diff\u00e9rentielle.<\/li>\n<li>Les corps de fonctions alg\u00e9briques: nombre de points rationnels pour des tours optimales explicites&nbsp;; applications \u00e0 la conception d&#8217;algorithmiques rapides pour la multiplication sur les corps finis&nbsp;; construction effective d&#8217;algorithmes de multiplication&nbsp;; construction de courbes alg\u00e9briques d\u00e9finies sur les corps finis avec un grand nombre de points rationnels.<\/li>\n<li>L&#8217;\u00e9tude des polyn\u00f4mes \u00e0 valeurs enti\u00e8res et questions voisines&nbsp;: description des propri\u00e9t\u00e9s alg\u00e9briques de polyn\u00f4mes \u00e0 valeurs enti\u00e8res et construction de \u00ab&nbsp;bonnes&nbsp;\u00bb bases&nbsp;; factorielles g\u00e9n\u00e9ralis\u00e9es de Bhargava&nbsp;; fonctions enti\u00e8res arithm\u00e9tiques dans des corps de fonctions, th\u00e9or\u00e8mes de type Gelfond&nbsp;; corps de Polya, Schinzel et Newton&nbsp;; groupe de Polya des corps de nombres.<\/li>\n<li>Aspects algorithmiques de la cohomologie des groupes arithm\u00e9tiques et des formes modulaires.<\/li>\n<\/ul>\n<p><\/p>","protected":false},"author":57,"featured_media":1190,"template":"","coauthors":[176,361],"class_list":["post-431","laboratoire","type-laboratoire","status-publish","has-post-thumbnail","hentry","entry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>GAATI \u2014 G\u00e9om\u00e9trie Alg\u00e9brique et Applications \u00e0 la Th\u00e9orie de l\u2019Information &#8226;<\/title>\n<meta name=\"description\" content=\"D\u00e9couvrir le laboratoire de G\u00e9om\u00e9trie Alg\u00e9brique et Applications \u00e0 la Th\u00e9orie de l&#039;Information de l&#039;Universit\u00e9 de la Polyn\u00e9sie fran\u00e7aise.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/recherche.upf.pf\/ty\/laboratoire\/gaati\/\" \/>\n<meta property=\"og:locale\" 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