{"id":1942,"date":"2023-06-08T17:08:49","date_gmt":"2023-06-08T15:08:49","guid":{"rendered":"https:\/\/web.umons.ac.be\/fs\/?p=1942"},"modified":"2023-06-08T17:10:56","modified_gmt":"2023-06-08T15:10:56","slug":"un-ancien-etudiant-de-la-faculte-des-sciences-de-lumons-se-distingue-par-ses-travaux-a-letranger","status":"publish","type":"post","link":"https:\/\/web.umons.ac.be\/fs\/fr\/un-ancien-etudiant-de-la-faculte-des-sciences-de-lumons-se-distingue-par-ses-travaux-a-letranger\/","title":{"rendered":"Un ancien \u00e9tudiant de la Facult\u00e9 des Sciences de l&rsquo;UMONS se distingue par ses travaux \u00e0 l&rsquo;\u00e9tranger"},"content":{"rendered":"<p>Le 5 juin 2023, la une (math\u00e9matique) du journal international <a href=\"https:\/\/www.quantamagazine.org\/\" target=\"_blank\" rel=\"noopener\">Quanta Magazine, <\/a><span style=\"font-size: 14px\">un p\u00e9riodique num\u00e9rique ind\u00e9pendant de la Fondation Simons (aux Etats-Unis) <\/span>a \u00e9t\u00e9 consacr\u00e9e aux recherches d&rsquo;un ancien \u00e9tudiant de la Facult\u00e9 des Sciences de l&rsquo;UMONS, <a href=\"https:\/\/www.maths.ox.ac.uk\/people\/cedric.pilatte\" target=\"_blank\" rel=\"noopener\">C\u00e9dric Pilatte<\/a>.<\/p>\n<p>Actuellement en doctorat \u00e0 l&rsquo;Universit\u00e9 d&rsquo;Oxford, le petit-fils d&rsquo;Andr\u00e9 Pilatte (doyen \u00e9m\u00e9rite de la La Facult\u00e9 Polytechnique de l&rsquo;UMONS) s&rsquo;est attaqu\u00e9 \u00e0 une conjecture. En math\u00e9matiques, il s&rsquo;agit d&rsquo;une assertion pour laquelle on ne conna\u00eet pas encore de d\u00e9monstration, mais que l&rsquo;on croit fortement \u00eatre vraie.<\/p>\n<p>Dans ce cas-ci, C\u00e9dric s&rsquo;est int\u00e9ress\u00e9 aux ensembles de Sidon, ensembles constitu\u00e9s de nombres entiers positifs v\u00e9rifiant que toutes les sommes de deux quelconques de ces entiers sont distinctes.<\/p>\n<p>A travers ses travaux, C\u00e9dric a prouv\u00e9 qu&rsquo;il \u00e9tait possible de cr\u00e9er un ensemble (une collection de nombres) qui satisfait deux propri\u00e9t\u00e9s apparemment incompatibles:<\/p>\n<ul>\n<li>La premi\u00e8re propri\u00e9t\u00e9 est qu&rsquo;il n&rsquo;y a pas deux paires de nombres dans l&rsquo;ensemble qui totalisent la m\u00eame somme. Par exemple, si vous additionnez deux nombres de {1, 3, 5, 11}, vous obtiendrez toujours un nombre unique. Plus le nombre d&rsquo;\u00e9l\u00e9ments augmente, plus la probabilit\u00e9 que les sommes co\u00efncident augmente, d\u00e9truisant de facto le caract\u00e8re \u00ab\u00a0Sidon\u00a0\u00bb de la collection de nombres.<\/li>\n<li>Concernant la deuxi\u00e8me propri\u00e9t\u00e9, il faut que que l&rsquo;ensemble soit tr\u00e8s grand. Il doit \u00eatre infini et vous devez \u00eatre en mesure de g\u00e9n\u00e9rer tout nombre suffisamment grand en additionnant au plus trois nombres de l&rsquo;ensemble.<\/li>\n<\/ul>\n<figure id=\"attachment_1945\" aria-describedby=\"caption-attachment-1945\" style=\"width: 302px\" class=\"wp-caption alignleft\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1945 \" src=\"https:\/\/web.umons.ac.be\/app\/uploads\/sites\/11\/2023\/06\/Photo-Cedric-300x195.jpg\" alt=\"\" width=\"302\" height=\"196\" srcset=\"https:\/\/web.umons.ac.be\/app\/uploads\/sites\/11\/2023\/06\/Photo-Cedric-300x195.jpg 300w, https:\/\/web.umons.ac.be\/app\/uploads\/sites\/11\/2023\/06\/Photo-Cedric-1024x665.jpg 1024w, https:\/\/web.umons.ac.be\/app\/uploads\/sites\/11\/2023\/06\/Photo-Cedric-768x498.jpg 768w, https:\/\/web.umons.ac.be\/app\/uploads\/sites\/11\/2023\/06\/Photo-Cedric-1017x660.jpg 1017w, https:\/\/web.umons.ac.be\/app\/uploads\/sites\/11\/2023\/06\/Photo-Cedric-30x19.jpg 30w, https:\/\/web.umons.ac.be\/app\/uploads\/sites\/11\/2023\/06\/Photo-Cedric-60x39.jpg 60w, https:\/\/web.umons.ac.be\/app\/uploads\/sites\/11\/2023\/06\/Photo-Cedric-360x234.jpg 360w, https:\/\/web.umons.ac.be\/app\/uploads\/sites\/11\/2023\/06\/Photo-Cedric.jpg 1074w\" sizes=\"auto, (max-width: 302px) 100vw, 302px\" \/><figcaption id=\"caption-attachment-1945\" class=\"wp-caption-text\">Cr\u00e9dit photo: Evan Nedyalkov<\/figcaption><\/figure>\n<p>Tout le probl\u00e8me pour C\u00e9dric \u00e9tait de d\u00e9montrer l&rsquo;existence d&rsquo;un tel ensemble de Sidon en\u00a0 v\u00e9rifiant que tout entier positif, sauf un nombre fini, est la somme de trois de ces entiers.<\/p>\n<p>Quoique l&rsquo;\u00e9nonc\u00e9 soit relativement simple \u00e0 comprendre, comme pour de nombreux probl\u00e8mes de th\u00e9orie des nombres, la preuve de C\u00e9dric n\u00e9cessite des outils math\u00e9matiques profonds alliant notamment probabilit\u00e9s et g\u00e9om\u00e9trique alg\u00e9brique.<\/p>\n<p>C\u00e9dric Pilatte a \u00e9t\u00e9 dipl\u00f4m\u00e9\u00a0 en 2019 du Bachelier en sciences math\u00e9matiques de l&rsquo;UMONS \u00e0 l&rsquo;issue d&rsquo;un parcours brillant, pendant lequel il a commenc\u00e9 la recherche dans le service de Logique Math\u00e9matique. Il a ensuite int\u00e9gr\u00e9, via la s\u00e9lection internationale, l&rsquo;Ecole Normale Sup\u00e9rieur de Paris. Il a \u00e9t\u00e9 dipl\u00f4m\u00e9 de l&rsquo;ENS en 2022.<\/p>\n<p>Pendant son Master \u00e0 Paris, il a r\u00e9alis\u00e9 des travaux sous la direction de Tim Gowers (m\u00e9daill\u00e9 Fields 1998) et de James Maynard.<\/p>\n<p>C\u00e9dric est actuellement \u00e9tudiant en doctorat \u00e0 l&rsquo;Universit\u00e9 d&rsquo;Oxford, sous la direction des professeurs James Maynard (m\u00e9daill\u00e9 Fields 2022) et de Ben Green.<\/p>\n<p>Retrouvez l&rsquo;article consacr\u00e9 \u00e0 C\u00e9dric Pilatte <a href=\"https:\/\/www.quantamagazine.org\/first-year-graduate-finds-paradoxical-number-set-20230605\/\" target=\"_blank\" rel=\"noopener\">ici.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>C\u00e9dric Pilatte, un ancien \u00e9tudiant\u00a0du D\u00e9partement de Math\u00e9matique\u00a0de la Facult\u00e9 des Sciences de l&rsquo;UMONS, vient d&rsquo;\u00eatre mis \u00e0 l&rsquo;honneur dans les pages de Quanta magazine, un p\u00e9riodique num\u00e9rique qui couvre les d\u00e9veloppements en physique, math\u00e9matiques, biologie et informatique. Une belle reconnaissance pour ce doctorant \u00e0 l&rsquo;Universit\u00e9 d&rsquo;Oxford. <\/p>\n","protected":false},"author":232,"featured_media":1945,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[97],"tags":[],"class_list":["post-1942","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-recherche"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Un ancien \u00e9tudiant de la Facult\u00e9 des Sciences de l&#039;UMONS se distingue par ses travaux \u00e0 l&#039;\u00e9tranger - Facult\u00e9 \/ FS<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/web.umons.ac.be\/fs\/fr\/un-ancien-etudiant-de-la-faculte-des-sciences-de-lumons-se-distingue-par-ses-travaux-a-letranger\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Un ancien \u00e9tudiant de la Facult\u00e9 des Sciences de l&#039;UMONS se distingue par ses travaux \u00e0 l&#039;\u00e9tranger - Facult\u00e9 \/ FS\" \/>\n<meta property=\"og:description\" content=\"C\u00e9dric Pilatte, un ancien \u00e9tudiant\u00a0du D\u00e9partement de Math\u00e9matique\u00a0de la Facult\u00e9 des Sciences de l&#039;UMONS, vient d&#039;\u00eatre mis \u00e0 l&#039;honneur dans les pages de Quanta magazine, un p\u00e9riodique num\u00e9rique qui couvre les d\u00e9veloppements en physique, math\u00e9matiques, biologie et informatique. Une belle reconnaissance pour ce doctorant \u00e0 l&#039;Universit\u00e9 d&#039;Oxford.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/web.umons.ac.be\/fs\/fr\/un-ancien-etudiant-de-la-faculte-des-sciences-de-lumons-se-distingue-par-ses-travaux-a-letranger\/\" \/>\n<meta property=\"og:site_name\" content=\"Facult\u00e9 \/ FS\" \/>\n<meta property=\"article:published_time\" content=\"2023-06-08T15:08:49+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-06-08T15:10:56+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/web.umons.ac.be\/app\/uploads\/sites\/11\/2023\/06\/Photo-Cedric.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1074\" \/>\n\t<meta property=\"og:image:height\" content=\"697\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Christophe Morel\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u00c9crit par\" \/>\n\t<meta name=\"twitter:data1\" content=\"Christophe Morel\" \/>\n\t<meta name=\"twitter:label2\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/web.umons.ac.be\/fs\/fr\/un-ancien-etudiant-de-la-faculte-des-sciences-de-lumons-se-distingue-par-ses-travaux-a-letranger\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/web.umons.ac.be\/fs\/fr\/un-ancien-etudiant-de-la-faculte-des-sciences-de-lumons-se-distingue-par-ses-travaux-a-letranger\/\"},\"author\":{\"name\":\"Christophe Morel\",\"@id\":\"https:\/\/web.umons.ac.be\/fs\/#\/schema\/person\/bb9799a3348930a3ddf84ceed54001c2\"},\"headline\":\"Un ancien \u00e9tudiant de la Facult\u00e9 des Sciences de l&rsquo;UMONS se distingue par ses travaux \u00e0 l&rsquo;\u00e9tranger\",\"datePublished\":\"2023-06-08T15:08:49+00:00\",\"dateModified\":\"2023-06-08T15:10:56+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/web.umons.ac.be\/fs\/fr\/un-ancien-etudiant-de-la-faculte-des-sciences-de-lumons-se-distingue-par-ses-travaux-a-letranger\/\"},\"wordCount\":502,\"commentCount\":0,\"image\":{\"@id\":\"https:\/\/web.umons.ac.be\/fs\/fr\/un-ancien-etudiant-de-la-faculte-des-sciences-de-lumons-se-distingue-par-ses-travaux-a-letranger\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/web.umons.ac.be\/app\/uploads\/sites\/11\/2023\/06\/Photo-Cedric.jpg\",\"articleSection\":[\"Recherche\"],\"inLanguage\":\"fr-FR\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/web.umons.ac.be\/fs\/fr\/un-ancien-etudiant-de-la-faculte-des-sciences-de-lumons-se-distingue-par-ses-travaux-a-letranger\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/web.umons.ac.be\/fs\/fr\/un-ancien-etudiant-de-la-faculte-des-sciences-de-lumons-se-distingue-par-ses-travaux-a-letranger\/\",\"url\":\"https:\/\/web.umons.ac.be\/fs\/fr\/un-ancien-etudiant-de-la-faculte-des-sciences-de-lumons-se-distingue-par-ses-travaux-a-letranger\/\",\"name\":\"Un ancien \u00e9tudiant de la Facult\u00e9 des Sciences de l'UMONS se distingue par ses travaux \u00e0 l'\u00e9tranger - 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