{"id":8849,"date":"2023-04-29T10:14:21","date_gmt":"2023-04-29T08:14:21","guid":{"rendered":"https:\/\/www.dm.unipi.it\/eventi\/tba-patrick-brosnan-university-of-maryland\/"},"modified":"2023-06-13T21:02:28","modified_gmt":"2023-06-13T19:02:28","slug":"tba-patrick-brosnan-university-of-maryland","status":"publish","type":"unipievents","link":"https:\/\/www.dm.unipi.it\/en\/eventi\/tba-patrick-brosnan-university-of-maryland\/","title":{"rendered":"Why Markman saves the Hodge conjecture for Weil type cycles from Kontsevich (in dimension 4) &#8211; Patrick Brosnan (University of Maryland)"},"content":{"rendered":"<h4>Venue<\/h4>\n<p>Department of Mathematics, Aula Seminari.<\/p>\n<h4 class='mt-4'>Abstract<\/h4>\n<p><span style=\"font-size:10pt\">I&#8217;ll explain two opposing pieces of work:&nbsp;&nbsp;<\/span><\/p>\n<p><span style=\"font-size:10pt\">(1) Markman&#8217;s proof of the<\/span><br \/><span style=\"font-size:10pt\">Hodge conjecture for general Weil type abelian fourfolds of discriminant 1, and<\/span>&nbsp;<\/p>\n<p><span style=\"font-size:10pt\">(2) Kontsevich&#8217;s tropical approach to finding a counterexample to the Hodge<\/span><br \/><span style=\"font-size:10pt\">conjecture for Weil type abelian varieties.&nbsp;&nbsp;<\/span><\/p>\n<p><span style=\"font-size:10pt\">Then I&#8217;ll explain why Markman&#8217;s proof of the Hodge conjecture in the discriminant 1 case rules out Kontsevich&#8217;s approach in dimension 4 (for arbitrary discriminant).<\/span><\/p>\n<p class='mt-4'>Further information is available on the <a href=\"https:\/\/events.dm.unipi.it\/event\/189\/\">event page<\/a> on the Indico platform.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>I&#8217;ll explain two opposing pieces of work:\u00a0\u00a0(1) Markman&#8217;s proof of theHodge conjecture for general Weil type abelian fourfolds of discriminant 1, and\u00a0(2) Kontsevich&#8217;s tropical approach to finding a counterexample to the Hodgeconjecture for Weil type&hellip;<\/p>\n<p><a class=\"btn btn-dark btn-sm unipi-read-more-link\" href=\"https:\/\/www.dm.unipi.it\/en\/eventi\/tba-patrick-brosnan-university-of-maryland\/\">Read More&#8230;<\/a><\/p>\n","protected":false},"author":6,"featured_media":0,"template":"","tags":[],"unipievents_taxonomy":[],"class_list":["post-8849","unipievents","type-unipievents","status-publish","hentry"],"acf":[],"unipievents_startdate":1687359600,"unipievents_enddate":1687363200,"unipievents_place":"Department of Mathematics, Aula Seminari.","unipievents_externalid":189,"jetpack_sharing_enabled":true,"publishpress_future_workflow_manual_trigger":{"enabledWorkflows":[]},"_links":{"self":[{"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/unipievents\/8849","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/unipievents"}],"about":[{"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/types\/unipievents"}],"author":[{"embeddable":true,"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/users\/6"}],"version-history":[{"count":2,"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/unipievents\/8849\/revisions"}],"predecessor-version":[{"id":9307,"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/unipievents\/8849\/revisions\/9307"}],"wp:attachment":[{"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/media?parent=8849"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/tags?post=8849"},{"taxonomy":"unipievents_taxonomy","embeddable":true,"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/unipievents_taxonomy?post=8849"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}