{"id":1464,"date":"2025-05-28T22:12:27","date_gmt":"2025-05-28T20:12:27","guid":{"rendered":"https:\/\/kleineberg.co.uk\/CTS-2025\/?post_type=mp-event&#038;p=1464"},"modified":"2025-06-05T14:42:19","modified_gmt":"2025-06-05T12:42:19","slug":"atul-shekhar","status":"publish","type":"mp-event","link":"https:\/\/kleineberg.co.uk\/CTS-2025\/timetable\/event\/atul-shekhar\/","title":{"rendered":"Atul Shekhar"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Asymptotics of expected number of components for random lemniscate with iid roots<\/h2>\n\n\n\n<p>For a random polynomial with iid roots in a disc, we consider its level sets (aka lemniscates). We obtain asymptotics for the expected number of connected components. This number shows a phase transition as the radius of the disc approaches one. At the critical value R=1, it behaves like \u221an. This behaviour can be accredited to a pairing phenomenon between roots and critical points of the given polynomial. This talk is based on an ongoing joint work with Koushik Ramachandran and Subhajit Ghosh.<\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Asymptotics of expected number of components for random lemniscate with iid roots For a random polynomial with iid roots in a disc, we consider its level sets (aka lemniscates). We obtain asymptotics for the expected number of connected components. This number shows a phase transition as the radius of the disc approaches one. At the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","mp-event_category":[15],"mp-event_tag":[],"class_list":["post-1464","mp-event","type-mp-event","status-publish","hentry","mp-event_category-speaker","entry","mp-event-item"],"_links":{"self":[{"href":"https:\/\/kleineberg.co.uk\/CTS-2025\/wp-json\/wp\/v2\/mp-event\/1464","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/kleineberg.co.uk\/CTS-2025\/wp-json\/wp\/v2\/mp-event"}],"about":[{"href":"https:\/\/kleineberg.co.uk\/CTS-2025\/wp-json\/wp\/v2\/types\/mp-event"}],"author":[{"embeddable":true,"href":"https:\/\/kleineberg.co.uk\/CTS-2025\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kleineberg.co.uk\/CTS-2025\/wp-json\/wp\/v2\/comments?post=1464"}],"wp:attachment":[{"href":"https:\/\/kleineberg.co.uk\/CTS-2025\/wp-json\/wp\/v2\/media?parent=1464"}],"wp:term":[{"taxonomy":"mp-event_category","embeddable":true,"href":"https:\/\/kleineberg.co.uk\/CTS-2025\/wp-json\/wp\/v2\/mp-event_category?post=1464"},{"taxonomy":"mp-event_tag","embeddable":true,"href":"https:\/\/kleineberg.co.uk\/CTS-2025\/wp-json\/wp\/v2\/mp-event_tag?post=1464"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}