{"id":1096,"date":"2022-04-21T23:53:12","date_gmt":"2022-04-22T06:53:12","guid":{"rendered":"https:\/\/math.berkeley.edu\/wp\/apde\/?p=1096"},"modified":"2022-04-21T23:53:12","modified_gmt":"2022-04-22T06:53:12","slug":"hong-wang-ucla","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/apde\/2022\/04\/21\/hong-wang-ucla\/","title":{"rendered":"Hong Wang (UCLA)"},"content":{"rendered":"\n\t\t\t\t\n<p>The APDE seminar on Monday, 4\/25, will be given by Hong Wang (UCLA) 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>:\u00a0Distance\u00a0sets\u00a0spanned\u00a0by\u00a0sets\u00a0of\u00a0dimension\u00a0d\/2<\/p>\n\n\n\n<p><strong>Abstract<\/strong>: Suppose that E is a subset of $\\mathbb{R}^{d}$, its distance set is defined as $\\Delta(E):=\\{ |x-y|, x, y \\in E \\}$.\u00a0 Joint with Pablo Shmerkin, we prove that if the packing dimension and Hausdorff dimension of $E$ both equal to $d\/2$, then $\\dim_{H} \\Delta(E) = 1$.\u00a0<br><\/p>\n\n\n\n<p>We also prove that if $\\dim_{H} E \\geq d\/2$, then $\\dim_{H} \\Delta(E) \\geq d\/2 + c_{d}$ when $d = 2, 3$; and $\\underline{dim}_{B} \\Delta(E) \\geq d\/2 + c_{d}$ when $d &gt; 3$ \u00a0for some explicit constants $c_{d}$.<\/p>\n\n\n\n<p><\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The APDE seminar on Monday, 4\/25, will be given by Hong Wang (UCLA) online via Zoom from 4:10pm to 5:00pm PST. To participate, email Sung-Jin Oh (sjoh@math.berkeley.edu). Title:\u00a0Distance\u00a0sets\u00a0spanned\u00a0by\u00a0sets\u00a0of\u00a0dimension\u00a0d\/2 Abstract: Suppose that E is a subset of $\\mathbb{R}^{d}$, its distance set is defined as $\\Delta(E):=\\{ |x-y|, x, y \\in E \\}$.\u00a0 Joint with Pablo Shmerkin, we [&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-1096","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1096","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=1096"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1096\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=1096"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=1096"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=1096"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}