{"id":2185,"date":"2021-10-28T10:49:49","date_gmt":"2021-10-28T07:49:49","guid":{"rendered":"https:\/\/mathematics.haifa.ac.il\/?p=2185"},"modified":"2021-11-04T12:16:57","modified_gmt":"2021-11-04T10:16:57","slug":"u-haifa-topology-geometry-seminar-sunday-oct-31-2021-speaker-philippe-charron-technion-pleijels-theorem-for-schrodinger-operators","status":"publish","type":"post","link":"https:\/\/mathematics.haifa.ac.il\/?p=2185","title":{"rendered":"U. Haifa Topology &#038; Geometry seminar: Sunday, OCT 31, 2021. Speaker: Philippe Charron (Technion). &#8220;Pleijel&#8217;s theorem for Schr\u00f6dinger operators&#8221;"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><strong>Time: <\/strong>Sunday, Oct. 31st, 17:00<br><strong>Location: <\/strong>On Zoom and in Room 614 Haifa University Mathematics and Science Building<br><strong>Speaker: <\/strong>Philippe Charron (Technion)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Zoom recording:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/us02web.zoom.us\/rec\/share\/nTEecWyLErYjpRjDfvxPASSzEj9Hy4pu4C4tjVVJudtLZ-tUwjR3knb_vbe7nTLP.0WWEpalVf2X4D9Ee\">https:\/\/us02web.zoom.us\/rec\/share\/nTEecWyLErYjpRjDfvxPASSzEj9Hy4pu4C4tjVVJudtLZ-tUwjR3knb_vbe7nTLP.0WWEpalVf2X4D9Ee<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Title: <\/strong>Pleijel&#8217;s theorem for Schr\u00f6dinger operators<br>We will discuss some recent results regarding the number of nodal domains of Laplace and Schr\u00f6dinger operators. Improving on Courant&#8217;s seminal work, Pleijel&#8217;s original proof in 1956 was only for domains in R^2 with Dirichlet boundary conditions, but it was later generalized to manifolds (Peetre and B\u00e9rard-Meyer) with Dirichlet boundary conditions, then to planar domains with Neumann Boundary conditions (Polterovich, L\u00e9na), but also to the quantum harmonic oscillator (C.) and to Schr\u00f6dinger operators with radial potentials (C. &#8211; Helffer &#8211; Hoffmann-Ostenhof). In this recent work, we proved Pleijel&#8217;s asymptotic upper bound for a much larger class of Schr\u00f6dinger operators which are not necessarily radial. In this talk, I will explain the problems that arise from studying Schr\u00f6dinger operators as well as the successive improvements in the methods that led to the current results.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>ZOOM COORDINATES:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-embed\"><div class=\"wp-block-embed__wrapper\">\nhttps:\/\/us02web.zoom.us\/j\/84987591026?pwd=aTJWcFlOSldKck5leGt2d25CYkRqZz09\n<\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Meeting ID: 849 8759 1026<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Time: Sunday, Oct. 31st, 17:00Location: On Zoom and in Room 614 Haifa University Mathematics and Science BuildingSpeaker: Philippe Charron (Technion) Zoom recording: https:\/\/us02web.zoom.us\/rec\/share\/nTEecWyLErYjpRjDfvxPASSzEj9Hy4pu4C4tjVVJudtLZ-tUwjR3knb_vbe7nTLP.0WWEpalVf2X4D9Ee Title: Pleijel&#8217;s theorem for Schr\u00f6dinger operatorsWe will discuss some recent results regarding the number of nodal domains&#8230;<br \/><a class=\"read-more-button\" href=\"https:\/\/mathematics.haifa.ac.il\/?p=2185\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6,4],"tags":[],"class_list":["post-2185","post","type-post","status-publish","format-standard","hentry","category-gt-seminar","category-seminar"],"_links":{"self":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/2185","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2185"}],"version-history":[{"count":4,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/2185\/revisions"}],"predecessor-version":[{"id":2191,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/2185\/revisions\/2191"}],"wp:attachment":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2185"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2185"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2185"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}