{"id":5067,"date":"2023-06-30T08:37:08","date_gmt":"2023-06-30T12:37:08","guid":{"rendered":"http:\/\/matroidunion.org\/?p=5067"},"modified":"2023-07-06T21:45:48","modified_gmt":"2023-07-07T01:45:48","slug":"online-talk-george-drummond","status":"publish","type":"post","link":"https:\/\/matroidunion.org\/?p=5067","title":{"rendered":"Online Talk: George Drummond"},"content":{"rendered":"\n<p><strong>YouTube recording:\u00a0<\/strong><a href=\"https:\/\/www.youtube.com\/watch?v=th_Vmb7qRwQ\" target=\"_blank\" rel=\"noopener\">https:\/\/www.youtube.com\/watch?v=th_Vmb7qRwQ<\/a><\/p>\n<p><strong>Time: <\/strong>Thursday, July 6, 3pm ET<br \/><strong>Zoom: <\/strong><a href=\"https:\/\/gatech.zoom.us\/j\/8802082683\" target=\"_blank\" rel=\"noopener\">https:\/\/gatech.zoom.us\/j\/8802082683<\/a><\/p>\n<p><strong>Speaker:\u00a0<\/strong>George Drummond, University of Canterbury<br \/><strong>Title: <\/strong>Elastic elements and where to find them<br \/><br \/><strong>Abstract: <\/strong>In this talk we will discuss the presence of &#8220;elastic&#8221; elements in 3-connected matroids. An element e of a 3-connected matroid M is\u00a0<i>elastic<\/i>\u00a0if both the simplification of M\/e and the\u00a0cosimplification of M\\e are 3-connected. Those familiar with Bixby&#8217;s Lemma will recall that at least one of these two conditions holds for every element. We will consider the obstructions to the presence of elastic elements, namely 4-element fans and another family of 3-separating structures we dub &#8220;theta-separators&#8221;, before arriving at our wheels-and-whirls-type theorem for elastic elements. In particular, it is shown that if neither of the aforementioned obstructions is present, then we are guaranteed at least four elastic elements. This\u00a0wheels-and-whirls-type result then extends naturally to a splitter theorem, where the removal of elements is with respect to elasticity and keeping a specified 3-connected minor. We will also consider some applications of these results to the related study of removing elements relative to a fixed basis.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>YouTube recording:\u00a0https:\/\/www.youtube.com\/watch?v=th_Vmb7qRwQ Time: Thursday, July 6, 3pm ETZoom: https:\/\/gatech.zoom.us\/j\/8802082683 Speaker:\u00a0George Drummond, University of CanterburyTitle: Elastic elements and where to find them Abstract: In this talk we will discuss the presence of &#8220;elastic&#8221; elements in 3-connected matroids. An element e of &hellip; <a href=\"https:\/\/matroidunion.org\/?p=5067\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":21,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[11],"class_list":["post-5067","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\/5067","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\/21"}],"replies":[{"embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5067"}],"version-history":[{"count":5,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/5067\/revisions"}],"predecessor-version":[{"id":5100,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/5067\/revisions\/5100"}],"wp:attachment":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5067"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5067"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5067"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}