{"id":2621,"date":"2020-06-16T10:13:00","date_gmt":"2020-06-16T14:13:00","guid":{"rendered":"http:\/\/matroidunion.org\/?p=2621"},"modified":"2020-07-13T09:37:25","modified_gmt":"2020-07-13T13:37:25","slug":"online-talk-matthew-kwan","status":"publish","type":"post","link":"https:\/\/matroidunion.org\/?p=2621","title":{"rendered":"Online talk: Matthew Kwan"},"content":{"rendered":"\n<p><strong>Mon, June 22,<\/strong> 3pm ET (8pm BST, 7am Tue NZST)<br \/><a href=\"http:\/\/web.stanford.edu\/~mattkwan\/\"><strong>Matthew Kwan<\/strong><\/a>, Stanford University<br \/><strong>Halfway to Rota&#8217;s basis conjecture<\/strong><br \/><a href=\"https:\/\/www.youtube.com\/watch?v=Qqq-Lr789qc\"><b>Youtube<\/b><\/a><\/p>\n<p><strong>Abstract:<br \/><\/strong>In 1989, Rota made the following conjecture. Given $n$ bases $B_1,\\ldots,B_n$ in an $n$-dimensional vector space $V$, one can always find $n$ disjoint bases of $V$, each containing exactly one element from each $B_i$ (we call such bases transversal bases). Rota&#8217;s basis conjecture remains wide open despite its apparent simplicity and the efforts of many researchers. In this talk we introduce the conjecture and its generalisation to matroids, and we outline a proof of the result that one can always find $(1\/2\u2212o(1))n$ disjoint transversal bases (improving on the previous record of $\\Omega(n\/\\log{n})$). This talk will be accessible to non-matroid theorists.<\/p>\n<p>Joint work with Matija Bucic, Alexey Pokrovskiy, and Benny Sudakov.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Mon, June 22, 3pm ET (8pm BST, 7am Tue NZST)Matthew Kwan, Stanford UniversityHalfway to Rota&#8217;s basis conjectureYoutube Abstract:In 1989, Rota made the following conjecture. Given $n$ bases $B_1,\\ldots,B_n$ in an $n$-dimensional vector space $V$, one can always find $n$ disjoint &hellip; <a href=\"https:\/\/matroidunion.org\/?p=2621\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[11],"class_list":["post-2621","post","type-post","status-publish","format-standard","hentry","category-matroids","tag-online-talks"],"_links":{"self":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/2621","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2621"}],"version-history":[{"count":5,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/2621\/revisions"}],"predecessor-version":[{"id":2725,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/2621\/revisions\/2725"}],"wp:attachment":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2621"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2621"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2621"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}