{"id":4951,"date":"2010-09-22T11:13:27","date_gmt":"2010-09-22T11:13:27","guid":{"rendered":"http:\/\/coates.ma.ic.ac.uk\/fanosearch\/?p=4951"},"modified":"2010-09-22T11:31:27","modified_gmt":"2010-09-22T11:31:27","slug":"l-katzarkov-gaps-spectra-and-applications","status":"publish","type":"post","link":"http:\/\/coates.ma.ic.ac.uk\/fanosearch\/?p=4951","title":{"rendered":"L. Katzarkov: &#8220;Gaps, Spectra, and Applications&#8221;"},"content":{"rendered":"<p>Here are my notes from Katzarkov&#8217;s talk in Bonn:<\/p>\n<p><a href=\"http:\/\/coates.ma.ic.ac.uk\/fanosearch\/wp-content\/uploads\/2010\/09\/Katzarkov_Bonn_Sep_2010.pdf\">Katzarkov_Bonn_Sep_2010<\/a><\/p>\n<p>Summary:<\/p>\n<ul>\n<li>Clemens-Griffiths showed that the 3-dimensional cubic is not rational by showing that its intermediate Jacobian is not the Jacobian of a curve; we suggest analogs of this.<\/li>\n<li>Homological Mirror Symmetry and the perverse sheaf of vanishing cycles<\/li>\n<li>detecting rationality via monodromy properties on the LG mirror (Gross-Katzarkov, Pryzalkowski, Golyshev)<\/li>\n<li>spectra of triangulated categories; examples<\/li>\n<li>Theorem: <img src='http:\/\/coates.ma.ic.ac.uk\/fanosearch\/wp-content\/latex\/021\/02129bb861061d1a052c592e2dc6b383-ffffff-000000-0.png' alt='X' title='X' class='latex' \/> is rational of dimension <img src='http:\/\/coates.ma.ic.ac.uk\/fanosearch\/wp-content\/latex\/7b8\/7b8b965ad4bca0e41ab51de7b31363a1-ffffff-000000-0.png' alt='n' title='n' class='latex' \/> implies that the spectrum of <img src='http:\/\/coates.ma.ic.ac.uk\/fanosearch\/wp-content\/latex\/a39\/a3948ad0cdc6fa96349fd5016bea3cb1-ffffff-000000-0.png' alt='D^b(X)' title='D^b(X)' class='latex' \/> has no gaps of size greaeter than <img src='http:\/\/coates.ma.ic.ac.uk\/fanosearch\/wp-content\/latex\/ba8\/ba81144e78f150a37fbe511667f9594b-ffffff-000000-0.png' alt='n-2' title='n-2' class='latex' \/><\/li>\n<li>the outlook for 4-dimensional cubics<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Here are my notes from Katzarkov&#8217;s talk in Bonn: Katzarkov_Bonn_Sep_2010 Summary: Clemens-Griffiths showed that the 3-dimensional cubic is not rational by showing that its intermediate Jacobian is not the Jacobian of a curve; we suggest analogs of this. Homological Mirror Symmetry and the perverse sheaf of vanishing cycles detecting rationality via monodromy properties on the [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[13,12],"class_list":["post-4951","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-bonn","tag-talk-notes"],"_links":{"self":[{"href":"http:\/\/coates.ma.ic.ac.uk\/fanosearch\/index.php?rest_route=\/wp\/v2\/posts\/4951","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/coates.ma.ic.ac.uk\/fanosearch\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/coates.ma.ic.ac.uk\/fanosearch\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/coates.ma.ic.ac.uk\/fanosearch\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/coates.ma.ic.ac.uk\/fanosearch\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4951"}],"version-history":[{"count":2,"href":"http:\/\/coates.ma.ic.ac.uk\/fanosearch\/index.php?rest_route=\/wp\/v2\/posts\/4951\/revisions"}],"predecessor-version":[{"id":4961,"href":"http:\/\/coates.ma.ic.ac.uk\/fanosearch\/index.php?rest_route=\/wp\/v2\/posts\/4951\/revisions\/4961"}],"wp:attachment":[{"href":"http:\/\/coates.ma.ic.ac.uk\/fanosearch\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4951"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/coates.ma.ic.ac.uk\/fanosearch\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4951"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/coates.ma.ic.ac.uk\/fanosearch\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4951"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}