{"id":42,"date":"2021-01-18T08:47:35","date_gmt":"2021-01-18T07:47:35","guid":{"rendered":"http:\/\/www.arthurtouati.fr\/?page_id=42"},"modified":"2026-06-22T09:54:14","modified_gmt":"2026-06-22T07:54:14","slug":"research","status":"publish","type":"page","link":"https:\/\/www.arthurtouati.fr\/index.php\/research\/","title":{"rendered":"Research"},"content":{"rendered":"\r\n<p>I am working in the fields of <strong>general relativity<\/strong> and <strong>wave turbulence<\/strong>. Here is a list of my collaborators:<\/p>\r\n<ul>\r\n<li><a href=\"https:\/\/sites.google.com\/site\/annsodspa\/\" target=\"_blank\" rel=\"noopener\">Anne-Sophie de Suzzoni<\/a><\/li>\r\n<li><a href=\"https:\/\/sites.google.com\/view\/ajfang\/\" target=\"_blank\" rel=\"noopener\">Allen Juntao Fang<\/a><\/li>\r\n<li><a href=\"https:\/\/perso.pages.math.cnrs.fr\/users\/annalaura.stingo\/\" target=\"_blank\" rel=\"noopener\">Annalaura Stingo<\/a><\/li>\r\n<li><a href=\"https:\/\/www.ljll.math.upmc.fr\/szeftel\/index.html.fr\" target=\"_blank\" rel=\"noopener\">J\u00e9r\u00e9mie Szeftel<\/a><\/li>\r\n<\/ul>\r\n<p>Below you\u2019ll find my articles and preprints, as well as proceedings, surveys. A list of the talks I have given at seminars or conferences is available in my CV (see the homepage).<\/p>\r\n<h2 class=\"has-text-color wp-block-heading\" style=\"color: #467599; text-align: center;\"><span style=\"color: #0a51b5;\">Articles &amp; preprints<\/span><\/h2>\r\n<div class=\"page\" title=\"Page 4\">\r\n<div class=\"layoutArea\">\r\n<div class=\"column\">\r\n<p>In reverse chronological order taking into account the first release on arXiv.<\/p>\r\n<p><span style=\"color: #0a51b5;\"><strong>9. \u00a0 <a href=\"https:\/\/arxiv.org\/abs\/2601.04117\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #03224c;\">Teukolsky on slowly-rotating Kerr-de Sitter in the vanishing <\/span><\/a><\/strong><\/span><span style=\"color: #03224c;\"><a href=\"https:\/\/arxiv.org\/abs\/2601.04117\" target=\"_blank\" rel=\"noopener\"><strong>\u039b limit <\/strong><\/a><span style=\"color: #000000;\">(with Allen Juntao Fang and J\u00e9r\u00e9mie Szeftel) 2026<\/span><strong>.<\/strong><\/span><\/p>\r\n<p><span style=\"color: #0a51b5;\"><strong>8.<\/strong><\/span> \u00a0 <a href=\"https:\/\/arxiv.org\/abs\/2503.24222\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #03224c;\"><strong>Wave turbulence for a semilinear Klein-Gordon system<\/strong><\/span><\/a> (with Anne-Sophie de Suzzoni and Annalaura Stingo) 2025.<\/p>\r\n<p><span style=\"color: #0a51b5;\"><strong>7.<\/strong><\/span> \u00a0 <span style=\"color: #03224c;\"><strong><a href=\"https:\/\/arxiv.org\/abs\/2405.02071\" target=\"_blank\" rel=\"noopener\">Spacelike initial data for black hole stability<\/a> <\/strong><\/span>(with Allen Juntao Fang and J\u00e9r\u00e9mie Szeftel) <em><i>Communications in Mathematical Physics<\/i><\/em>, 406(10), 235, 2025.<\/p>\r\n<p><span style=\"color: #0a51b5;\"><strong>6.<\/strong><\/span> \u00a0 <a href=\"https:\/\/arxiv.org\/abs\/2402.17530\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #03224c;\"><strong>The reverse Burnett conjecture for null dusts<\/strong><\/span><\/a> <em>Annals of PDE<\/em>, 11(2), 22, 2025.<\/p>\r\n<p><span style=\"color: #0a51b5;\"><strong>5.<\/strong><\/span> \u00a0 <span style=\"color: #03224c;\"><strong><a href=\"https:\/\/arxiv.org\/abs\/2401.14353\" target=\"_blank\" rel=\"noopener\">Initial data for Minkowski stability with arbitrary decay<\/a> <\/strong><\/span><span style=\"color: #03224c;\"><span style=\"color: #000000;\">(wi<\/span><\/span>th Allen Juntao Fang and J\u00e9r\u00e9mie Szeftel) <em>Advances in Theoretical Mathematical Physics,<\/em> 29(4):933-1043, 2025.<\/p>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p><span style=\"color: #0a51b5;\"><strong>4.<\/strong><\/span> \u00a0\u00a0<span style=\"color: #03224c;\"><a href=\"https:\/\/arxiv.org\/abs\/2206.13062\" target=\"_blank\" rel=\"noopener\"><strong>High-frequency solutions to the constraint equations<\/strong><\/a><\/span><em>\u00a0<\/em><em><i>Communications in Mathematical Physics, <\/i><\/em>402(1):97-140, 2023<em><i>.<\/i><\/em><\/p>\r\n<p><span style=\"color: #0a51b5;\"><strong>3.<\/strong><\/span> \u00a0 <strong><span style=\"color: #03224c;\"><a href=\"https:\/\/arxiv.org\/abs\/2206.12318\" target=\"_blank\" rel=\"noopener\">Geometric optics approximation for the Einstein vacuum equations<\/a><\/span>\u00a0<\/strong><em><i>Communications in Mathematical Physics, <\/i><\/em>402(3):3109-3200, 2023.<\/p>\r\n<p><span style=\"color: #0a51b5;\"><strong>2.<\/strong><\/span> \u00a0\u00a0<span style=\"color: #03224c;\"><strong><a href=\"https:\/\/arxiv.org\/abs\/2109.15204\" target=\"_blank\" rel=\"noopener\">Global existence of high-frequency solutions to a semi-linear wave equation with a null structure<\/a> <\/strong><\/span><em>Asymptotic Analysis,\u00a0<\/em>131(3-4):541-582, 2023.<\/p>\r\n<p><span style=\"color: #0a51b5;\"><strong>1.<\/strong><\/span> \u00a0 <span style=\"color: #03224c;\"><strong><a href=\"https:\/\/arxiv.org\/abs\/2101.09093\" target=\"_blank\" rel=\"noopener\">Einstein vacuum equations with <span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"texatom\"><span id=\"MathJax-Span-4\" class=\"mrow\"><span id=\"MathJax-Span-5\" class=\"mi\">\ud835\udd4c<\/span><\/span><\/span><span id=\"MathJax-Span-6\" class=\"mo\">(<\/span><span id=\"MathJax-Span-7\" class=\"mn\">1<\/span><span id=\"MathJax-Span-8\" class=\"mo\">)<\/span><\/span><\/span><\/span> symmetry in an elliptic gauge: local well-posedness and blow-up criterium<\/a>\u00a0<\/strong><\/span><em>Journal of Hyperbolic Differential Equations,\u00a0<\/em>19(04):635-715, 2022.<\/p>\r\n<p>Articles 2, 3 and 4 of this list constitute my <a href=\"https:\/\/www.arthurtouati.fr\/wp-content\/uploads\/2022\/10\/manuscrit-final.pdf\" target=\"_blank\" rel=\"noopener\">PhD thesis<\/a>, which starts with an introduction written in French.<\/p>\r\n<p>&nbsp;<\/p>\r\n<h2 class=\"has-text-color\" style=\"color: #467599; text-align: center;\"><span style=\"color: #0a51b5;\">Proceedings &amp; surveys<\/span><\/h2>\r\n<p><span style=\"color: #0a51b5;\"><strong>2. \u00a0 <span style=\"color: #03224c;\"><a href=\"https:\/\/comptes-rendus.academie-sciences.fr\/mecanique\/item\/CRMECA_2025__353_G1_455_0\/\" target=\"_blank\" rel=\"noopener\">Burnett&rsquo;s conjecture in general relativity<\/a> <\/span><\/strong><span style=\"color: #000000;\"><em>Recent advances in general relativity: an issue in memory of Yvonne Choquet-Bruhat, Comptes Rendus M\u00e9canique<\/em>, Volume 353, pp 455-476, 2025.<\/span><\/span><\/p>\r\n<p><span style=\"color: #0a51b5;\"><strong>1.<\/strong><\/span> \u00a0\u00a0<strong><a href=\"https:\/\/proceedings.centre-mersenne.org\/articles\/10.5802\/slsedp.159\/\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #03224c;\">Geometric optics approximation for the Einstein vacuum equations<\/span><\/a><i>\u00a0<\/i><\/strong><em>S\u00e9minaire Laurent Schwartz \u2014 EDP et applications<\/em>, Expos\u00e9 no. 7, 12 p. (2022-2023).<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>&nbsp;<\/p>\r\n","protected":false},"excerpt":{"rendered":"<p>I am working in the fields of general relativity and wave turbulence. Here is a list of my collaborators: Anne-Sophie de Suzzoni Allen Juntao Fang Annalaura Stingo J\u00e9r\u00e9mie Szeftel Below you\u2019ll find my articles and preprints, as well as proceedings, surveys. A list of the talks I have given at seminars or conferences is available [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-42","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.arthurtouati.fr\/index.php\/wp-json\/wp\/v2\/pages\/42","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.arthurtouati.fr\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.arthurtouati.fr\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.arthurtouati.fr\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.arthurtouati.fr\/index.php\/wp-json\/wp\/v2\/comments?post=42"}],"version-history":[{"count":216,"href":"https:\/\/www.arthurtouati.fr\/index.php\/wp-json\/wp\/v2\/pages\/42\/revisions"}],"predecessor-version":[{"id":686,"href":"https:\/\/www.arthurtouati.fr\/index.php\/wp-json\/wp\/v2\/pages\/42\/revisions\/686"}],"wp:attachment":[{"href":"https:\/\/www.arthurtouati.fr\/index.php\/wp-json\/wp\/v2\/media?parent=42"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}