{"id":1117,"date":"2022-09-13T11:12:28","date_gmt":"2022-09-13T18:12:28","guid":{"rendered":"https:\/\/math.berkeley.edu\/wp\/apde\/?p=1117"},"modified":"2022-09-13T11:12:28","modified_gmt":"2022-09-13T18:12:28","slug":"thibault-lefevre-sorbonne-u","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/apde\/2022\/09\/13\/thibault-lefevre-sorbonne-u\/","title":{"rendered":"Thibault Lefeuvre (Sorbonne U)"},"content":{"rendered":"\n\t\t\t\t\n<p>The APDE seminar on Monday, 9\/19, will be given by Thibault Lefeuvre (Sorbonne U) in-person in <strong>Evans 740,<\/strong> and will also be broadcasted online via Zoom from <strong>4:10pm to 5:00pm PST<\/strong>. To participate, email Sung-Jin Oh (sjoh@math.berkeley.edu).<\/p>\n\n\n\n<p><strong>Title<\/strong>: On isospectral connections<\/p>\n\n\n\n<p><strong>Abstract<\/strong>: Kac\u2019s celebrated inverse spectral question \u201cCan one hear the shape of a drum?\u201d consists in recovering a metric from the knowledge of the<br> spectrum of its Laplacian. I will discuss a very similar question on negatively-curved manifolds, where the word \u201cmetric\u201d is now replaced by \u201cconnection\u201d on a vector bundle. This problem turns out to be very rich and connects unexpectedly to two other a priori unrelated fields of<br> mathematics:<br>1) in dynamical systems: the study of the ergodic behaviour of partially hyperbolic flows obtained as isometric extensions of the geodesic flow (over negatively-curved Riemannian manifolds);<br>2) in algebraic geometry: the classification of non-trivial algebraic maps between spheres.<br><br>Using this relation, I will explain a positive answer to Kac\u2019s inverse spectral problem for connections under a low rank assumption. Joint work with Mihajlo Ceki\u0107.<\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The APDE seminar on Monday, 9\/19, will be given by Thibault Lefeuvre (Sorbonne U) in-person in Evans 740, and will also be broadcasted online via Zoom from 4:10pm to 5:00pm PST. To participate, email Sung-Jin Oh (sjoh@math.berkeley.edu). Title: On isospectral connections Abstract: Kac\u2019s celebrated inverse spectral question \u201cCan one hear the shape of a drum?\u201d [&hellip;]<\/p>\n","protected":false},"author":106,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1117","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1117","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/users\/106"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/comments?post=1117"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1117\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=1117"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=1117"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=1117"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}