{"id":1224,"date":"2023-08-24T08:23:41","date_gmt":"2023-08-24T15:23:41","guid":{"rendered":"https:\/\/math.berkeley.edu\/wp\/apde\/?p=1224"},"modified":"2023-08-24T08:23:41","modified_gmt":"2023-08-24T15:23:41","slug":"junehyuk-jung-brown","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/apde\/2023\/08\/24\/junehyuk-jung-brown\/","title":{"rendered":"Junehyuk Jung (Brown)"},"content":{"rendered":"\n\t\t\t\t\n<p>The APDE seminar on Monday, 9\/18, will be given by Junehyuk Jung (Brown) in-person in\u00a0<strong>Evans 736,<\/strong>\u00a0and will also be broadcasted online via Zoom from\u00a0<strong>4:10pm to 5:00pm PST<\/strong>. To participate, please email Federico Pasqualotto (fpasqualotto@berkeley.edu) or Mengxuan Yang (mxyang@math.berkeley.edu).<\/p>\n\n\n\n<p><strong>Title:<\/strong> Nodal domains of equivariant eigenfunctions on Kaluza-Klein 3-folds.<\/p>\n\n\n\n<p><strong>Abstract:<\/strong> In this talk, I&#8217;m going to present my work with Steve Zelditch, where we prove that, when M is a principle $S^1$-bundle equipped with a generic Kaluza-Klein metric, the nodal counting of eigenfunctions is typically 2, independent of the eigenvalues. Note that principle S1-bundle equipped with a Kaluza-Klein metric never admits ergodic geodesic flow. This, for instance, contrasts the case when (M,g) is a surface with non-empty boundary with ergodic geodesic flow (billiard flow), in which case the number of nodal domains of typical eigenfunctions tends to +\u221e. I will also present an orthonormal eigenbasis of Laplacian on a flat 3-torus, where every non-constant eigenfunction has exactly two nodal domains. In particular, this tells us that the number of nodal domain could be uniformly bounded independent of the eigenvalue.<\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The APDE seminar on Monday, 9\/18, will be given by Junehyuk Jung (Brown) in-person in\u00a0Evans 736,\u00a0and will also be broadcasted online via Zoom from\u00a04:10pm to 5:00pm PST. To participate, please email Federico Pasqualotto (fpasqualotto@berkeley.edu) or Mengxuan Yang (mxyang@math.berkeley.edu). Title: Nodal domains of equivariant eigenfunctions on Kaluza-Klein 3-folds. Abstract: In this talk, I&#8217;m going to present [&hellip;]<\/p>\n","protected":false},"author":102,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1224","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1224","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\/102"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/comments?post=1224"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1224\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=1224"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=1224"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=1224"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}