{"id":1418,"date":"2025-09-25T10:54:44","date_gmt":"2025-09-25T17:54:44","guid":{"rendered":"https:\/\/wp.math.berkeley.edu\/hades\/?p=1418"},"modified":"2025-09-25T10:56:30","modified_gmt":"2025-09-25T17:56:30","slug":"random-tensors-and-fractional-nls","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2025\/09\/25\/random-tensors-and-fractional-nls\/","title":{"rendered":"Random tensors and fractional NLS"},"content":{"rendered":"<p>The HADES seminar on Tuesday, <strong>September<\/strong><strong> 30th<\/strong>, will be at <strong>3:30pm<\/strong>\u00a0in\u00a0<strong>Room 740<\/strong>.<\/p>\n<p><strong>Speaker:\u00a0<\/strong>Rui Liang<\/p>\n<p><strong>Abstract:<\/strong>In this talk, we will consider the Schr\u00f6dinger equation with cubic nonlinearity on the circle, with initial data distributed according to the Gibbs measure.\u00a0 We will discuss the challenges and strategies involved in establishing the Poincar\u00e9 recurrence property with respect to the Gibbs measure in the full dispersive range. This work, using the theory of the random averaging operator developed by Deng-Nahmod-Yue &#8217;19, addresses an open question proposed by Sun-Tzvetkov &#8217;21. We will also explain why the Gibbs dynamics for the full dispersive range is sharp in some sense. Finally, we will see how the theory of random tensors works for extending this work to multi-dimensional settings.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday, September 30th, will be at 3:30pm\u00a0in\u00a0Room 740. Speaker:\u00a0Rui Liang Abstract:In this talk, we will consider the Schr\u00f6dinger equation with cubic nonlinearity on the circle, with initial data distributed according to the Gibbs measure.\u00a0 We will discuss the challenges and strategies involved in establishing the Poincar\u00e9 recurrence property with respect to [&hellip;]<\/p>\n","protected":false},"author":116,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[25],"tags":[],"class_list":["post-1418","post","type-post","status-publish","format-standard","hentry","category-fall-2025"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1418","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/users\/116"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=1418"}],"version-history":[{"count":2,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1418\/revisions"}],"predecessor-version":[{"id":1422,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1418\/revisions\/1422"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=1418"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=1418"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=1418"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}