{"id":543,"date":"2022-10-10T21:00:38","date_gmt":"2022-10-11T04:00:38","guid":{"rendered":"\/wp\/hades\/?p=543"},"modified":"2022-10-10T21:00:38","modified_gmt":"2022-10-11T04:00:38","slug":"a-fractal-uncertainty-principle-for-discrete-2d-cantor-sets","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2022\/10\/10\/a-fractal-uncertainty-principle-for-discrete-2d-cantor-sets\/","title":{"rendered":"A fractal uncertainty principle for discrete 2D Cantor sets"},"content":{"rendered":"\n\t\t\t\t\n<p> The HADES seminar on Tuesday, <strong>October 18th<\/strong>&nbsp;will be at&nbsp;<strong>3:30 pm<\/strong> over zoom. Zoom link:<a href=\"https:\/\/berkeley.zoom.us\/j\/96232331895\">https:\/\/berkeley.zoom.us\/j\/96232331895<\/a>.    <\/p>\n\n\n\n<p><strong>Speaker:<\/strong> Alex Cohen<\/p>\n\n\n\n<p><strong>Abstract:<\/strong> A fractal uncertainty principle (FUP) states that a function $f$ and its Fourier transform cannot both be large on a fractal set. These were recently introduced by Semyon Dyatlov and collaborators in order to prove new results in quantum chaos. So far FUPs are only understood for fractal sets in $\\mathbb{R}$, and fractal sets in $\\mathbb{R}^2$ remain elusive. In this talk, we prove a sharp fractal uncertainty principle for Cantor sets in $\\mathbb{Z}\/N\\mathbb{Z} \\times \\mathbb{Z}\/N\\mathbb{Z}$, a discrete model for $\\mathbb{R}^2$. The main tool is a quantitative form of Lang&#8217;s conjecture from number theory due to Beukers and Smyth. <\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday, October 18th&nbsp;will be at&nbsp;3:30 pm over zoom. Zoom link:https:\/\/berkeley.zoom.us\/j\/96232331895. Speaker: Alex Cohen Abstract: A fractal uncertainty principle (FUP) states that a function $f$ and its Fourier transform cannot both be large on a fractal set. These were recently introduced by Semyon Dyatlov and collaborators in order to prove new results [&hellip;]<\/p>\n","protected":false},"author":88,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-543","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/543","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\/88"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=543"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/543\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=543"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=543"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=543"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}