{"id":536,"date":"2022-10-02T18:31:49","date_gmt":"2022-10-03T01:31:49","guid":{"rendered":"\/wp\/hades\/?p=536"},"modified":"2022-10-02T18:31:49","modified_gmt":"2022-10-03T01:31:49","slug":"a-proto-inverse-szemeredi-trotter-theorem","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2022\/10\/02\/a-proto-inverse-szemeredi-trotter-theorem\/","title":{"rendered":"A Proto Inverse Szemer\u00e9di&#8211;Trotter Theorem"},"content":{"rendered":"\n\t\t\t\t\n<p class=\"wp-block-paragraph\"> The HADES seminar on Tuesday, <strong>October 4th<\/strong>&nbsp;will be at&nbsp;<strong>3:30 pm<\/strong>&nbsp;in&nbsp;<strong>Room 740<\/strong>.    <\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Speaker:<\/strong> Olivine Silier<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Abstract:<\/strong> A point-line <strong>incidence<\/strong> is a point-line pair such that the point is on the line. The <strong>Szemer\u00e9di&#8211;Trotter<\/strong> theorem says the number of point-line incidences for $n$ (distinct) points and lines in $\\mathbb{R}^2$ is tightly upperbounded by $O(n^{4\/3})$. We advance the <strong>inverse problem<\/strong>: we geometrically characterize `sharp&#8217; examples which saturate the bound using the <strong>cell decomposition<\/strong> and <strong>crossing lemma<\/strong> proofs of Szemer\u00e9di&#8211;Trotter. This result is also an important step towards obtaining an $\\epsilon$ improvement in the <strong>unit-distance <\/strong>problem. (Ongoing work with Nets Katz)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><br>No background required, all welcome!<br><\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday, October 4th&nbsp;will be at&nbsp;3:30 pm&nbsp;in&nbsp;Room 740. Speaker: Olivine Silier Abstract: A point-line incidence is a point-line pair such that the point is on the line. The Szemer\u00e9di&#8211;Trotter theorem says the number of point-line incidences for $n$ (distinct) points and lines in $\\mathbb{R}^2$ is tightly upperbounded by $O(n^{4\/3})$. We advance the [&hellip;]<\/p>\n","protected":false},"author":88,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-536","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/536","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\/88"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=536"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/536\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=536"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=536"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=536"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}