{"id":4737,"date":"2023-02-08T08:39:25","date_gmt":"2023-02-08T13:39:25","guid":{"rendered":"http:\/\/matroidunion.org\/?p=4737"},"modified":"2023-02-23T09:38:53","modified_gmt":"2023-02-23T14:38:53","slug":"online-talk-relinde-jurrius-3","status":"publish","type":"post","link":"https:\/\/matroidunion.org\/?p=4737","title":{"rendered":"Online Talk: Relinde Jurrius"},"content":{"rendered":"\n<p><strong>YouTube recording: <\/strong><a href=\"https:\/\/www.youtube.com\/watch?v=6hmhSYado9Q\" target=\"_blank\" rel=\"noopener\">https:\/\/www.youtube.com\/watch?v=6hmhSYado9Q<\/a><strong><br \/><br \/>Time: <\/strong>Thursday, Feb 16, 3pm EST (8pm GMT, 9am Fri NZDT)<br \/><strong>Zoom: <\/strong><a href=\"https:\/\/gatech.zoom.us\/j\/8802082683\">https:\/\/gatech.zoom.us\/j\/8802082683<\/a><br \/><br \/><strong>Speaker:<\/strong> <a href=\"https:\/\/www.relindejurrius.nl\/#about\" target=\"_blank\" rel=\"noopener\">Relinde Jurrius<\/a>, Netherlands Defense Academy<br \/><strong>Title: <\/strong>The combinatorial derived matroid<br \/><strong>Abstract: <\/strong>The question of &#8220;dependencies between dependencies&#8221; in matroids has been raised in the 1960&#8217;s by Rota and Crapo, in various formulations (here is a nice overview elsewhere on this blog: <a href=\"https:\/\/matroidunion.org\/?p=2628\" target=\"_blank\" rel=\"noopener\">matroidunion.org\/?p=2628<\/a>). For a matroid $M$, the <em>derived matroid<\/em> is a matroid that has as ground set the set of (co)circuits of $M$. Over time, various definitions of a derived matroid have been proposed. However, none of them completely solved the question of Rota and Crapo: these definitions depend on a representation, for example, or are not unique, or don&#8217;t always exist.<strong><br aria-hidden=\"true\" \/><\/strong>In a recent paper with Olga Kuznetsova and Ragnar Freij-Hollanti, we proposed a definition of a derived matroid that is purely combinatorial. The combinatorial derived matroid is defined via the rank function of $M$, and via an operation that resembles a closure operation on the collection of dependent sets. It is therefore uniquely defined for any matroid. In this talk I will motivate this definition and discuss some examples and desirable properties of this definition. Time permitting we will discuss open questions and links to previous definitions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>YouTube recording: https:\/\/www.youtube.com\/watch?v=6hmhSYado9Q Time: Thursday, Feb 16, 3pm EST (8pm GMT, 9am Fri NZDT)Zoom: https:\/\/gatech.zoom.us\/j\/8802082683 Speaker: Relinde Jurrius, Netherlands Defense AcademyTitle: The combinatorial derived matroidAbstract: The question of &#8220;dependencies between dependencies&#8221; in matroids has been raised in the 1960&#8217;s by &hellip; <a href=\"https:\/\/matroidunion.org\/?p=4737\">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-4737","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\/4737","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=4737"}],"version-history":[{"count":3,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/4737\/revisions"}],"predecessor-version":[{"id":4745,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/4737\/revisions\/4745"}],"wp:attachment":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4737"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4737"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4737"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}