{"id":1249,"date":"2025-02-15T18:23:38","date_gmt":"2025-02-16T02:23:38","guid":{"rendered":"https:\/\/wp.math.berkeley.edu\/hades\/?p=1249"},"modified":"2025-05-04T19:35:35","modified_gmt":"2025-05-05T02:35:35","slug":"lossless-strichartz-estimates-on-manifolds-with-trapping","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2025\/02\/15\/lossless-strichartz-estimates-on-manifolds-with-trapping\/","title":{"rendered":"Lossless Strichartz estimates on manifolds with trapping"},"content":{"rendered":"<p>The HADES seminar on Tuesday, <strong>February<\/strong><strong>\u00a018<\/strong><strong>th<\/strong>, will be at\u00a0<strong>3<\/strong><strong>:30pm<\/strong>\u00a0in\u00a0<strong>Room 740.<\/strong><\/p>\n<p><strong>Speaker:\u00a0<\/strong>Zhongkai Tao<\/p>\n<p><strong>Abstract: <\/strong>The Strichartz estimate\u00a0is an important estimate in proving the well-posedness of dispersive PDEs. People believed that the lossless Strichartz estimate could not hold on manifolds with trapping (for example, the local smoothing estimate always comes with a logarithmic loss in the presence of trapping). Surprisingly, in 2009, Burq, Guillarmou, and Hassell proved a lossless Strichartz estimate for manifolds with trapping under the &#8220;pressure condition&#8221;. I will talk about their result as well as our recent work with Xiaoqi Huang, Christopher Sogge, and Zhexing Zhang, which goes beyond the pressure condition using the fractal uncertainty principle and a logarithmic short-time Strichartz estimate.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday, February\u00a018th, will be at\u00a03:30pm\u00a0in\u00a0Room 740. Speaker:\u00a0Zhongkai Tao Abstract: The Strichartz estimate\u00a0is an important estimate in proving the well-posedness of dispersive PDEs. People believed that the lossless Strichartz estimate could not hold on manifolds with trapping (for example, the local smoothing estimate always comes with a logarithmic loss in the presence [&hellip;]<\/p>\n","protected":false},"author":95,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[22,1],"tags":[],"class_list":["post-1249","post","type-post","status-publish","format-standard","hentry","category-spring-2025","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1249","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\/95"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=1249"}],"version-history":[{"count":1,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1249\/revisions"}],"predecessor-version":[{"id":1250,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1249\/revisions\/1250"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=1249"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=1249"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=1249"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}