{"id":1958,"date":"2025-11-04T18:22:41","date_gmt":"2025-11-04T18:22:41","guid":{"rendered":"https:\/\/wp.math.berkeley.edu\/apde\/?p=1958"},"modified":"2025-11-04T18:22:41","modified_gmt":"2025-11-04T18:22:41","slug":"katya-krupchyk-uc-irvine","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/apde\/2025\/11\/04\/katya-krupchyk-uc-irvine\/","title":{"rendered":"Katya Krupchyk (UC Irvine)"},"content":{"rendered":"<p>The APDE seminar on Monday, 11\/10, will be given by Katya Krupchyk (UC Irvine) in-person in <strong>Evans 736,<\/strong>\u00a0and will also be broadcasted online via Zoom from\u00a0<strong>4:10pm to 5:00pm PDT<\/strong>. To participate, please email Adam Black (adamblack<span id=\"eeb-322338-403021\"><span id=\"eeb-843318-171438\"><span id=\"eeb-203570-882396\"><span id=\"eeb-990440-551518\"><span id=\"eeb-688663-335757\"><span id=\"eeb-951702-73120\"><span id=\"eeb-183542-482341\"><span id=\"eeb-725178-862757\"><span id=\"eeb-367675-784580\">@berkeley.edu<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>).<\/p>\n<p><strong>Title<\/strong>: Fractional Anisotropic Calder\u00f3n Problem<\/p>\n<p><strong>Abstract: <\/strong>The classical anisotropic Calder\u00f3n problem, in its geometric formulation, asks whether a Riemannian metric, or more generally a compact Riemannian manifold with boundary, can be recovered from the Dirichlet-to-Neumann map for the Laplace\u2013Beltrami operator, given on the boundary of the manifold. The problem remains open in general for smooth metrics in dimensions three and higher.<br \/>\nIn this talk, we will present uniqueness results for the fractional anisotropic Calder\u00f3n problem, a nonlocal analogue of the classical anisotropic Calder\u00f3n problem, in dimensions two and higher, in two settings: on smooth closed Riemannian manifolds with source-to-solution data, and on domains in Euclidean space with external measurements. Specifically, we will show that the source-to-solution map for the fractional Laplace\u2013Beltrami operator, known on an arbitrary open subset of a smooth closed Riemannian manifold, determines the manifold up to isometry. In the Euclidean case, for smooth Riemannian metrics that coincide with the Euclidean metric outside a compact set, we will demonstrate that the partial exterior Dirichlet-to-Neumann map for the fractional Laplace\u2013Beltrami operator, known on arbitrary open subsets in the exterior of the domain, determines the Riemannian metric up to diffeomorphism fixing the exterior. The talk is based on joint works with Ali Feizmohammadi, Tuhin Ghosh, Angkana R\u00fcland, Johannes Sj\u00f6strand, and Gunther Uhlmann.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The APDE seminar on Monday, 11\/10, will be given by Katya Krupchyk (UC Irvine) in-person in Evans 736,\u00a0and will also be broadcasted online via Zoom from\u00a04:10pm to 5:00pm PDT. To participate, please email Adam Black (adamblack@berkeley.edu). Title: Fractional Anisotropic Calder\u00f3n Problem Abstract: The classical anisotropic Calder\u00f3n problem, in its geometric formulation, asks whether a Riemannian [&hellip;]<\/p>\n","protected":false},"author":119,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1958","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1958","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\/119"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/comments?post=1958"}],"version-history":[{"count":1,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1958\/revisions"}],"predecessor-version":[{"id":1959,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1958\/revisions\/1959"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=1958"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=1958"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=1958"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}