{"id":6800,"date":"2022-10-03T18:45:51","date_gmt":"2022-10-03T16:45:51","guid":{"rendered":"https:\/\/www.dm.unipi.it\/eventi\/collinearity-on-cubic-surfaces-jan-dobrowolski-university-of-manchester\/"},"modified":"2022-10-03T18:45:51","modified_gmt":"2022-10-03T16:45:51","slug":"collinearity-on-cubic-surfaces-jan-dobrowolski-university-of-manchester","status":"publish","type":"unipievents","link":"https:\/\/www.dm.unipi.it\/en\/eventi\/collinearity-on-cubic-surfaces-jan-dobrowolski-university-of-manchester\/","title":{"rendered":"Collinearity on cubic surfaces &#8211; Jan Dobrowolski (University of Manchester)"},"content":{"rendered":"<h4>Venue<\/h4>\n<p>Dipartimento di Matematica, Aula Seminari.<\/p>\n<h4 class='mt-4'>Abstract<\/h4>\n<div>We study the ternary relation R of collinearity between points of a smooth cubic surface X. Our aim is to understand sequences of triples (A,B,C) of finite sets with |A|=|B|=|C| whose Cartesian products have asymptotically maximal possible size of the intersection with the relation R (i.e. growing roughly as quickly as the square of the size of the sets A,B,C). This is an instance of the so-called&nbsp;Elekes-Szab\u00f3 problem. It is well-known that such configurations can be built on planar cubic curves, hence we can find them in an intersection of X with a plane. We prove that if X is smooth and irreducible, then actually any such configuration on X concentrates on its intersection with a plane, and if X is reducible the same holds in most cases.<\/div>\n<div>&nbsp;<\/div>\n<div>This is a joint work with Martin Bays and Tingxiang Zou.<\/div>\n<p class='mt-4'>Further information is available on the <a href=\"https:\/\/events.dm.unipi.it\/event\/122\/\">event page<\/a> on the Indico platform.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We study the ternary relation R of collinearity between points of a smooth cubic surface X. Our aim is to understand sequences of triples (A,B,C) of finite sets with |A|=|B|=|C| whose Cartesian products have asymptotically maximal possible size of&hellip;<\/p>\n<p><a class=\"btn btn-dark btn-sm unipi-read-more-link\" href=\"https:\/\/www.dm.unipi.it\/en\/eventi\/collinearity-on-cubic-surfaces-jan-dobrowolski-university-of-manchester\/\">Read More&#8230;<\/a><\/p>\n","protected":false},"author":6,"featured_media":0,"template":"","tags":[],"unipievents_taxonomy":[],"class_list":["post-6800","unipievents","type-unipievents","status-publish","hentry"],"acf":[],"unipievents_startdate":1668682800,"unipievents_enddate":1668686400,"unipievents_place":"Dipartimento di Matematica, Aula Seminari.","unipievents_externalid":122,"jetpack_sharing_enabled":true,"publishpress_future_workflow_manual_trigger":{"enabledWorkflows":[]},"_links":{"self":[{"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/unipievents\/6800","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":0,"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/unipievents\/6800\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/media?parent=6800"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/tags?post=6800"},{"taxonomy":"unipievents_taxonomy","embeddable":true,"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/unipievents_taxonomy?post=6800"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}