{"id":1351,"date":"2018-12-27T17:34:21","date_gmt":"2018-12-27T15:34:21","guid":{"rendered":"https:\/\/mathematics.haifa.ac.il\/?p=1351"},"modified":"2019-01-01T17:06:11","modified_gmt":"2019-01-01T15:06:11","slug":"colloquium-tuesday-january-1-2019-speaker-karim-adiprasito-hebrew-university-title-from-halls-marriage-theorem-to-algebraic-geometry-and-back-to-combinatorics","status":"publish","type":"post","link":"https:\/\/mathematics.haifa.ac.il\/?p=1351","title":{"rendered":"Colloquium: Tuesday, January 1, 2019. Speaker: Karim Adiprasito (Hebrew University). Title: &#8220;From Hall&#8217;s marriage theorem to algebraic geometry (and back to combinatorics)&#8221;."},"content":{"rendered":"<p>We discuss how something remarkably similar to Hall&#8217;s marriage theorem appears naturally in context of a conjecture of Grothendieck in algebraic geometry, and how this is useful to prove some long-standing problems in discrete geometry. For instance, I will prove that for a simplicial complex \u0394 that embeds into R^(2d), the number of d-dimensional simplices exceeds the number of (d\u22121)-dimensional simplices by a factor of at most d+2. This generalizes a result going back to Descartes and Euler, and resolves the Gr\u00fcnbaum-Kalai-Sarkaria conjecture.<\/p>\n<p>&nbsp;<\/p>\n<p>Tea will be served before the talk (at <strong>13:50<\/strong>).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We discuss how something remarkably similar to Hall&#8217;s marriage theorem appears naturally in context of a conjecture of Grothendieck in algebraic geometry, and how this is useful to prove some long-standing problems in discrete geometry. For instance, I will prove&#8230;<br \/><a class=\"read-more-button\" href=\"https:\/\/mathematics.haifa.ac.il\/?p=1351\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":["post-1351","post","type-post","status-publish","format-standard","hentry","category-colloquium"],"_links":{"self":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/1351","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1351"}],"version-history":[{"count":1,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/1351\/revisions"}],"predecessor-version":[{"id":1352,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/1351\/revisions\/1352"}],"wp:attachment":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1351"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1351"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1351"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}