{"id":1801,"date":"2025-03-04T16:10:01","date_gmt":"2025-03-04T16:10:01","guid":{"rendered":"https:\/\/wp.math.berkeley.edu\/apde\/?p=1801"},"modified":"2025-03-07T19:23:05","modified_gmt":"2025-03-07T19:23:05","slug":"pablo-shmerkin-university-of-brisith-columbia","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/apde\/2025\/03\/04\/pablo-shmerkin-university-of-brisith-columbia\/","title":{"rendered":"Pablo Shmerkin (University of British Columbia)"},"content":{"rendered":"<p>The APDE seminar on Monday, <span data-sheets-root=\"1\">3\/10<\/span>, will be given by Pablo Shmerkin (University of Brisith Columbia)in-person in <strong>Evans 736,<\/strong> and will also be broadcasted online via Zoom from <strong>4:10pm to 5:00pm PST<\/strong>. To participate, please email Anuj Kumar (anujkumar@berkeley.edu).<\/p>\n<p><strong>Title: <\/strong>Around the sum-product problem for fractals<\/p>\n<p><strong>Abstract: <\/strong>A fundamental result of Bourgain asserts, in its simplest form, that if $A$ is a Borel subset of the real line with Hausdorff dimension $s\\in (0,1)$, then $\\dim(A+A.A) \\ge s+c(s)$ for some small constant $c(s)&gt;0$. Note that this implies, in particular, that there exist no Borel subrings of the reals of intermediate dimension. I will present some recent variants and improvements on this result, including joint work (across several papers) with N. de Saxc\u00e9, T. Orponen and H. Wang.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The APDE seminar on Monday, 3\/10, will be given by Pablo Shmerkin (University of Brisith Columbia)in-person in Evans 736, and will also be broadcasted online via Zoom from 4:10pm to 5:00pm PST. To participate, please email Anuj Kumar (anujkumar@berkeley.edu). Title: Around the sum-product problem for fractals Abstract: A fundamental result of Bourgain asserts, in its [&hellip;]<\/p>\n","protected":false},"author":113,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1801","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1801","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\/113"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/comments?post=1801"}],"version-history":[{"count":3,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1801\/revisions"}],"predecessor-version":[{"id":1807,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1801\/revisions\/1807"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=1801"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=1801"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=1801"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}