October 3, 2024 (Thursday), 4:10 pm<\/p>\n
Mark Ellingham and Rares Rasdeaconu, Vanderbilt University<\/p>\n
\u201cMaximum genus directed embeddings of digraphs\u201d<\/strong><\/p>\n Mark Ellingham, Vanderbilt University<\/strong><\/p>\n In topological graph theory we often want to find embeddings of a given connected graph with minimum genus, so that the underlying compact orientable surface of the embedding is as simple as possible.\u00a0 If we restrict ourselves to cellular embeddings, where all faces are homeomorphic to disks, then it is also of interest to find embeddings with maximum genus.\u00a0 For undirected graphs this is a very well-solved problem.\u00a0 For digraphs we can consider directed embeddings, where each face is bounded by a directed walk in the digraph.\u00a0 Much less is known about maximum genus in this setting.\u00a0 Previous work by other people provided the answer in the very special case of regular tournaments, and in some cases of directed 4-regular graphs the answer can be found using an algorithm for the representable delta-matroid parity problem.\u00a0 We describe some recent work, joint with Joanna Ellis-Monaghan of the University of Amsterdam, where we have solved the maximum directed genus problem in some reasonably general situations.<\/p>\n <\/p>\n \u201cThe loss of maximality in Hilbert squares\u201d<\/strong><\/p>\n Rares Rasdeaconu, Vanderbilt University<\/strong><\/p>\n The talk will be an introduction to the Smith-Thom maximality of real algebraic manifolds. An unexpected loss of maximality for the Hilbert square of real algebraic manifolds exhibited in a joint work with V. Kharlamov (University of Strasbourg) will be discussed. Time permitting, I will outline several open problems.<\/p>\n","protected":false},"excerpt":{"rendered":" October 3, 2024 (Thursday), 4:10 pm Mark Ellingham and Rares Rasdeaconu, Vanderbilt University \u201cMaximum genus directed embeddings of digraphs\u201d Mark Ellingham, Vanderbilt University In topological graph theory we often want to find embeddings of a given connected graph with minimum genus, so that the underlying compact orientable surface of the embedding is as simple as…<\/p>\n","protected":false},"author":74,"featured_media":754,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[7],"tags":[],"acf":[],"jetpack_featured_media_url":"https:\/\/as.vanderbilt.edu\/math\/wp-content\/uploads\/sites\/69\/2024\/08\/colloquium.png","_links":{"self":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/426"}],"collection":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/users\/74"}],"replies":[{"embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/comments?post=426"}],"version-history":[{"count":2,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/426\/revisions"}],"predecessor-version":[{"id":668,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/426\/revisions\/668"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/media\/754"}],"wp:attachment":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/media?parent=426"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/categories?post=426"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/tags?post=426"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}