{"id":521,"date":"2018-01-18T15:09:40","date_gmt":"2018-01-18T23:09:40","guid":{"rendered":"https:\/\/math.berkeley.edu\/wp\/apde\/?p=521"},"modified":"2018-01-18T15:09:40","modified_gmt":"2018-01-18T23:09:40","slug":"semyon-dyatlov-uc-berkeley","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/apde\/2018\/01\/18\/semyon-dyatlov-uc-berkeley\/","title":{"rendered":"Semyon Dyatlov (UC Berkeley)"},"content":{"rendered":"<p>\t\t\t\tThe Analysis and PDE seminar will take place Monday, January 29, in 740 Evans from 4:10 to 5 pm.<\/p>\n<p>Title: Fourier dimension for limit sets<\/p>\n<p>Abstract: For a finite measure $\\mu$ on the real line, its Fourier dimension is defined using the rate of polynomial decay of the Fourier transform $\\hat \\mu$. The Fourier dimension of $\\mu$ may be much smaller than the Hausdorff dimension of the support of $\\mu$: a classical example is the Cantor measure on the mid-third Cantor set which has Fourier dimension equal to 0.<\/p>\n<p>I will present a joint result with J. Bourgain showing that the Patterson-Sullivan measure on the limit set of a convex co-compact group of fractional linear transformations has positive Fourier dimension. The proof uses advanced tools from additive combinatorics (the discretized sum-product theorem) and exploits the fact that fractional linear transformations are (generally) not linear. An application is a new spectral gap result for convex co-compact hyperbolic surfaces.\t\t<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Analysis and PDE seminar will take place Monday, January 29, in 740 Evans from 4:10 to 5 pm. Title: Fourier dimension for limit sets Abstract: For a finite measure $\\mu$ on the real line, its Fourier dimension is defined using the rate of polynomial decay of the Fourier transform $\\hat \\mu$. The Fourier dimension [&hellip;]<\/p>\n","protected":false},"author":107,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-521","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/521","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\/107"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/comments?post=521"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/521\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=521"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=521"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=521"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}