{"id":3432,"date":"2020-10-27T14:02:26","date_gmt":"2020-10-27T18:02:26","guid":{"rendered":"http:\/\/matroidunion.org\/?p=3432"},"modified":"2020-11-25T13:19:46","modified_gmt":"2020-11-25T18:19:46","slug":"online-talk-attila-joo","status":"publish","type":"post","link":"https:\/\/matroidunion.org\/?p=3432","title":{"rendered":"Online talk: Attila Jo\u00f3"},"content":{"rendered":"\n<h5><strong>Monday, November 2,<\/strong> <strong>3pm ET<\/strong> (8pm GMT, 9am Tue NZDT)<br \/><a href=\"https:\/\/www.math.uni-hamburg.de\/home\/joo\/\"><strong>Attila Jo\u00f3<\/strong><\/a>, University of Hamburg<br \/><strong>The Matroid Intersection Conjecture of Nash-Williams<br \/><\/strong><\/h5>\n<h5><a href=\"https:\/\/youtu.be\/wifVNTk_ZTQ\"><b>YouTube<\/b><\/a><\/h5>\n<h5>\u00a0<\/h5>\n<h5><b><\/b><strong>Abstract:<\/strong><\/h5>\n<p>Rado initiated a program in the 1960s\u00a0 to find the &#8220;right&#8221; infinite generalization of the matroid concept. The results of Higgs and Oxley and more recently Bruhn et al. led eventually to a positive answer for Rado&#8217;s question.\u00a0 One of the most important open problems in the theory of infinite matroids is the Matroid Intersection Conjecture of Nash-Williams which is a structural infinite generalization of the well-known Intersection Theorem of Edmonds. It says that if $M$ and $N$ are (finitary) matroids on the common edge set $E$, then they admit a common independent set $I$ that has a bipartition $I=I_M \\cup I_N$ with $cl_M(I_M) \\cup cl_N(I_N)=E$. The restriction of the conjecture to partition matroids (known as &#8216;K\u00f6nig&#8217;s Theorem for infinite bipartite graphs&#8217;) was proven by Aharoni, Nash-Williams and Shelah and is a deep result in infinite matching theory. In the main part of the talk we give a proof overview of our partial result which decides affirmatively the conjecture whenever $E$ is countable. Finally we reveal an unpublished conjecture of Aharoni about the intersection of more than two matroids which is wide open even for three finite matroids.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Monday, November 2, 3pm ET (8pm GMT, 9am Tue NZDT)Attila Jo\u00f3, University of HamburgThe Matroid Intersection Conjecture of Nash-Williams YouTube \u00a0 Abstract: Rado initiated a program in the 1960s\u00a0 to find the &#8220;right&#8221; infinite generalization of the matroid concept. The &hellip; <a href=\"https:\/\/matroidunion.org\/?p=3432\">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-3432","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\/3432","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=3432"}],"version-history":[{"count":7,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/3432\/revisions"}],"predecessor-version":[{"id":3505,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/3432\/revisions\/3505"}],"wp:attachment":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3432"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3432"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3432"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}