{"id":1082,"date":"2022-04-11T09:19:46","date_gmt":"2022-04-11T16:19:46","guid":{"rendered":"https:\/\/math.berkeley.edu\/wp\/apde\/?p=1082"},"modified":"2022-04-11T09:19:46","modified_gmt":"2022-04-11T16:19:46","slug":"malo-jezequel-mit","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/apde\/2022\/04\/11\/malo-jezequel-mit\/","title":{"rendered":"Malo J\u00e9z\u00e9quel (MIT)"},"content":{"rendered":"\n\t\t\t\t\n<p>The APDE seminar on Monday, 4\/11, will be given by <em>Malo J\u00e9z\u00e9quel<\/em> (MIT) both in-person (891 Evans) and online via Zoom from <strong>4:10pm to 5:00pm PST<\/strong>. To participate, email Sung-Jin Oh (sjoh@math.berkeley.edu).<\/p>\n\n\n\n<p><strong>Title<\/strong>: Semiclassical measures for higher dimensional quantum cat maps.<\/p>\n\n\n\n<p><strong>Abstract<\/strong>: Quantum chaos is the study of quantum systems whose<br>associated classical dynamics is chaotic. For instance, a central<br>question concerns the high frequencies behavior of the eigenstates of<br>the Laplace-Beltrami operator on a negatively curved compact<br>Riemannian manifold M. In that case, the associated classical dynamics<br>is the geodesic flow on the unit tangent bundle of M, which is<br>hyperbolic and hence chaotic. Quantum cat maps are a popular toy model<br>for this problem, in which the geodesic flow is replaced by a cat map,<br>i.e. the action on the torus of a matrix with integer coefficients. In<br>this talk, I will introduce quantum cat maps, and then discuss a<br>result on delocalization for the associated eigenstates. It is deduced<br>from a \\emph{fractal uncertainty principle}. Similar statements have<br>been obtained in the context of negatively curved surfaces by<br>Dyatlov-Jin and Dyatlov-Jin-Nonnenmacher, and the case of<br>two-dimensional cat maps have been dealt with by Schwartz. The novelty<br>of our result is that we are sometimes able to bypass the restriction<br>to low dimensions. This is a joint work with Semyon Dyatlov.<\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The APDE seminar on Monday, 4\/11, will be given by Malo J\u00e9z\u00e9quel (MIT) both in-person (891 Evans) and online via Zoom from 4:10pm to 5:00pm PST. To participate, email Sung-Jin Oh (sjoh@math.berkeley.edu). Title: Semiclassical measures for higher dimensional quantum cat maps. Abstract: Quantum chaos is the study of quantum systems whoseassociated classical dynamics is chaotic. [&hellip;]<\/p>\n","protected":false},"author":106,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1082","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1082","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/users\/106"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/comments?post=1082"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1082\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=1082"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=1082"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=1082"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}