{"id":425,"date":"2021-11-21T18:26:54","date_gmt":"2021-11-22T02:26:54","guid":{"rendered":"\/wp\/hades\/?p=425"},"modified":"2021-11-21T18:26:54","modified_gmt":"2021-11-22T02:26:54","slug":"decoupling-for-some-convex-sequences-in-mathbb-r","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2021\/11\/21\/decoupling-for-some-convex-sequences-in-mathbb-r\/","title":{"rendered":"Decoupling for some convex sequences in $\\mathbb R$"},"content":{"rendered":"\n\t\t\t\t\n<p>The HADES seminar on Tuesday,&nbsp;<strong>November 23rd<\/strong>, will be given by <font color=\"#191e23\"><span><b>Yuqiu Fu<\/b><\/span><\/font> at <strong>5 pm<\/strong>&nbsp;on Zoom.<\/p>\n\n\n\n<p><strong>Speaker<\/strong>: Yuqiu Fu (MIT)<\/p>\n\n\n\n<p><strong>Abstract<\/strong>: If the Fourier transform of a function $f:\\mathbb R \\rightarrow \\mathbb C$ is  supported in a neighborhood of an arithmetic progression, then $|f|$ is morally constant on translates of a neighborhood of a dual arithmetic progression.<br> We will discuss how this &#8220;locally constant property&#8221; allows us to prove sharp decoupling inequalities for functions on $\\mathbb R$ with Fourier support near certain convex\/concave sequence, where we cover segments of the sequence by neighborhoods of arithmetic progressions with increasing\/decreasing common difference. Examples of such sequences include $\\{\\frac{n^2}{N^2}\\}_{n=N+1}^{N+N^{1\/2}}$ and $\\{\\log n\\}_{n=N+1}^{N+N^{1\/2}}.$<br> The sequence $\\{\\log n\\}_{n=N+1}^{2N}$ is closely connected to Montgomery&#8217;s conjecture on Dirichlet polynomials but we see some difficulties in studying the decoupling for $\\{\\log n\\}_{n=N+1}^{2N}.$ This is joint work with Larry Guth and Dominique Maldague.<\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday,&nbsp;November 23rd, will be given by Yuqiu Fu at 5 pm&nbsp;on Zoom. Speaker: Yuqiu Fu (MIT) Abstract: If the Fourier transform of a function $f:\\mathbb R \\rightarrow \\mathbb C$ is supported in a neighborhood of an arithmetic progression, then $|f|$ is morally constant on translates of a neighborhood of a dual [&hellip;]<\/p>\n","protected":false},"author":90,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-425","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/425","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\/90"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=425"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/425\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=425"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=425"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=425"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}