{"id":4154,"date":"2021-07-21T11:56:02","date_gmt":"2021-07-21T15:56:02","guid":{"rendered":"http:\/\/matroidunion.org\/?p=4154"},"modified":"2021-07-30T03:43:48","modified_gmt":"2021-07-30T07:43:48","slug":"online-talk-matthew-sullivan","status":"publish","type":"post","link":"https:\/\/matroidunion.org\/?p=4154","title":{"rendered":"Online Talk: Matthew Sullivan"},"content":{"rendered":"\n<p><strong>Monday, July 26,<\/strong> <strong>3pm ET<\/strong> (8pm BST, 7am Tue NZST)<br \/><strong><a href=\"https:\/\/uwaterloo.ca\/combinatorics-and-optimization\/about\/people\/m8sulliv\">Matthew Sullivan<\/a>,<\/strong> University of Waterloo<br \/><strong>Rotation Systems and Simple Drawings of $K_n$<\/strong><\/p>\n<div><strong>YouTube: <\/strong><a href=\"https:\/\/youtu.be\/HRaqRGgdE-8\">https:\/\/youtu.be\/HRaqRGgdE-8<\/a><\/div>\n<h5>\u00a0<\/h5>\n<h5><b><\/b><strong>Abstract:<\/strong><\/h5>\n<h5>A <em>complete rotation system<\/em>\u00a0on $n$ vertices is a collection consisting of cyclic permutations of the elements $[n]\\backslash \\{i\\}$, one cyclic permutation for each $i$. If $D$ is a simple drawing of a labelled graph, then a rotation at vertex $v$ is the cyclic ordering of the edges at $v$. In particular, the collection of all vertex rotations of a simple drawing of $K_n$ is a rotation system.<\/h5>\n<h5>\u00a0<\/h5>\n<h5>If a complete rotation system can be represented by a simple drawing of $K_n$, then we call such a rotation system<em> realizable<\/em>. In 2011, Jan Kyn\u010dl published a proof using homotopy implying that if all 6 vertex rotation systems of an $n$ vertex rotation system $R_n$ are realizable, then $R_n$ is realizable.<\/h5>\n<h5>\u00a0<\/h5>\n<h5>In this talk, we will briefly review a full characterization of realizable rotation systems, present a structural characterization of edges and faces in simple drawings of $K_n$ and see a combinatorial proof of a weak characterization of realizable rotation systems.<\/h5>\n","protected":false},"excerpt":{"rendered":"<p>Monday, July 26, 3pm ET (8pm BST, 7am Tue NZST)Matthew Sullivan, University of WaterlooRotation Systems and Simple Drawings of $K_n$ YouTube: https:\/\/youtu.be\/HRaqRGgdE-8 \u00a0 Abstract: A complete rotation system\u00a0on $n$ vertices is a collection consisting of cyclic permutations of the elements &hellip; <a href=\"https:\/\/matroidunion.org\/?p=4154\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":20,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[11],"class_list":["post-4154","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\/4154","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\/20"}],"replies":[{"embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4154"}],"version-history":[{"count":3,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/4154\/revisions"}],"predecessor-version":[{"id":4169,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/4154\/revisions\/4169"}],"wp:attachment":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4154"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4154"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4154"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}