{"id":2527,"date":"2020-05-05T10:30:30","date_gmt":"2020-05-05T14:30:30","guid":{"rendered":"http:\/\/matroidunion.org\/?p=2527"},"modified":"2020-05-13T18:29:48","modified_gmt":"2020-05-13T22:29:48","slug":"online-talk-rudi-pendavingh-plus-an-announcement","status":"publish","type":"post","link":"https:\/\/matroidunion.org\/?p=2527","title":{"rendered":"Online talk: Rudi Pendavingh (plus an announcement)"},"content":{"rendered":"\n<p>I&#8217;m happy to announce another seminar series many of our readers may be interested in, titled &#8220;<a href=\"https:\/\/dibernstein.github.io\/VirtualSeminar.html\">Algebraic Matroids and Rigidity Theory&#8221;<\/a>. It is at 10am EST on Thursdays and is organized by Daniel Bernstein. Please email him at [dibernst ~at ~ mit ~.~ edu] or [bernstein.daniel ~at~ gmail ~.~ com] to get on the mailing list and for the password.<\/p>\n<p>We do not intend on having a talk on May 18 for <a href=\"https:\/\/en.wikipedia.org\/wiki\/Victoria_Day\">Victoria Day<\/a> :). Here&#8217;s the info for Rudi&#8217;s talk next week.<\/p>\n<p><strong>Mon, May 11<\/strong> 3pm EST (8pm BST, 7am Tue NZST)<br \/><a href=\"https:\/\/www.win.tue.nl\/~rudi\/index.html\"><strong>Rudi Pendavingh<\/strong><\/a>, Eindhoven University of Technology<br \/><strong>Counting valuated matroid types<\/strong><br \/><a href=\"https:\/\/www.youtube.com\/watch?v=wyXxQ9-QQJY\"><span style=\"color: #1b8be0;\"><b>YouTube<\/b><\/span><\/a><br \/><a href=\"https:\/\/matroidunion.org\/wp-content\/uploads\/2020\/05\/valuation-types-2.pdf\">Corrected slides<\/a><\/p>\n<p><strong>Abstract:<br \/><\/strong>If $M$ is a matroid with bases $\\mathcal{B}$, then a <em>valuation<\/em> of $M$ is a function $\\nu:\\mathcal{B}\\rightarrow \\mathbb{R}$ satisfying the following symmetric exchange axiom:<\/p>\n<div>\u00a0<\/div>\n<ul>\n<li>If $B, B\u2019\\in \\mathcal{B}$ and $e\\in B\\setminus B\u2019$, then there is an $f\\in B\u2019\\setminus B$ so that $$\\nu(B)+\\nu(B\u2019)\\leq \\nu(B-e+f)+\\nu(B\u2019+e-f)$$<\/li>\n<\/ul>\n<div>The <em>combinatorial type<\/em> of a given valuation essentially comprises the information for which $B,B\u2019,e,f$ equality is attained in this definition.\u00a0<\/div>\n<div>\u00a0<\/div>\n<div>A matroid is <em>rigid<\/em> if all its valuations are of the same combinatorial type. By a theorem of Lafforge, a rigid matroid has a discrete set of linear representations over each field. By work of Bollen, Draisma, and myself, a rigid matroid which is algebraic in characteristic $p$ is also linear in characteristic $p$. More generally, if a matroid is algebraic in characteristic $p$, then the matroid has some valuation which satisfies a certain condition on its combinatorial type. Testing this condition involved enumerating the combinatorial types.<\/div>\n<div>\u00a0<\/div>\n<div>In this talk, we present bounds on the number of combinatorial types of valuations. The method of proof suggests ways to enumerate the combinatorial types of valuations of a given matroid more efficiently.<\/div>\n<div>\u00a0<\/div>\n<div>This is joint work with Simon Soto Ochoa.<\/div>\n","protected":false},"excerpt":{"rendered":"<p>I&#8217;m happy to announce another seminar series many of our readers may be interested in, titled &#8220;Algebraic Matroids and Rigidity Theory&#8221;. It is at 10am EST on Thursdays and is organized by Daniel Bernstein. Please email him at [dibernst ~at &hellip; <a href=\"https:\/\/matroidunion.org\/?p=2527\">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-2527","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\/2527","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=2527"}],"version-history":[{"count":10,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/2527\/revisions"}],"predecessor-version":[{"id":2548,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/2527\/revisions\/2548"}],"wp:attachment":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2527"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2527"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2527"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}