{"id":1252,"date":"2023-10-18T17:03:57","date_gmt":"2023-10-19T00:03:57","guid":{"rendered":"https:\/\/math.berkeley.edu\/wp\/apde\/?p=1252"},"modified":"2023-10-18T17:03:57","modified_gmt":"2023-10-19T00:03:57","slug":"kevin-ren-princeton","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/apde\/2023\/10\/18\/kevin-ren-princeton\/","title":{"rendered":"Kevin Ren (Princeton)"},"content":{"rendered":"\n\t\t\t\t\n<p>The APDE seminar on Monday, 10\/23, will be given by Kevin Ren (Princeton) in-person in\u00a0<strong>Evans 736,<\/strong>\u00a0and will also be broadcasted online via Zoom from\u00a0<strong>4:10pm to 5:00pm PST<\/strong>. To participate, please email Federico Pasqualotto (fpasqualotto@berkeley.edu) or Mengxuan Yang (mxyang@math.berkeley.edu).<\/p>\n\n\n\n<p><strong>Title:<\/strong> Pinned Distances in R^d<\/p>\n\n\n\n<p><strong>Abstract:<\/strong> Given a set E in R^d with Hausdorff dimension &gt; d\/2, Falconer conjectured that the set of distances between any two points in E has positive Lebesgue measure. This conjecture remains open in all dimensions, despite significant progress in the last 30 years. Building upon this progress, we show that if d &gt;= 3 and dim_H (E) &gt; d\/2 + 1\/4 &#8211; 1\/(8d+4), then the distance set of E has positive Lebesgue measure. The proof uses a new radial projection theorem in R^d applied to a variant of a decoupling framework of Guth-Iosevich-Ou-Wang. Joint work with Xiumin Du, Yumeng Ou, and Ruixiang Zhang.<\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The APDE seminar on Monday, 10\/23, will be given by Kevin Ren (Princeton) in-person in\u00a0Evans 736,\u00a0and will also be broadcasted online via Zoom from\u00a04:10pm to 5:00pm PST. To participate, please email Federico Pasqualotto (fpasqualotto@berkeley.edu) or Mengxuan Yang (mxyang@math.berkeley.edu). Title: Pinned Distances in R^d Abstract: Given a set E in R^d with Hausdorff dimension &gt; d\/2, [&hellip;]<\/p>\n","protected":false},"author":102,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1252","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1252","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\/102"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/comments?post=1252"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1252\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=1252"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=1252"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=1252"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}