{"id":702,"date":"2025-07-31T16:10:38","date_gmt":"2025-07-31T20:10:38","guid":{"rendered":"https:\/\/eventos.cmm.uchile.cl\/pdeseminar\/?p=702"},"modified":"2025-07-31T16:10:38","modified_gmt":"2025-07-31T20:10:38","slug":"recent-progress-on-the-fractional-yamabe-problem","status":"publish","type":"post","link":"https:\/\/eventos.cmm.uchile.cl\/pdeseminar\/2025\/07\/recent-progress-on-the-fractional-yamabe-problem\/","title":{"rendered":"Recent Progress on the Fractional Yamabe Problem"},"content":{"rendered":"<h3 class=\"metadatos\">Speaker: <span style=\"color: #993300\"><strong>Sophie Aiken<\/strong><\/span><\/h3>\n<h3 class=\"metadatos\"><strong>University of California Santa Cruz<\/strong><\/h3>\n<h3 class=\"metadatos\">Date: <strong>December 02nd at 12:10 pm.<\/strong><\/h3>\n<div>\n<p><strong>Abstract :<\/strong> Let $(M^n, [\\hat{g}])$ be the conformal infinity of an asymptotically hyperbolic Einstein (AHE) manifold $(X^{n+1},g^+).$ We will take the scattering operator associated to the AHE filling in as the fractional conformal Laplacian. Equipped with fractional conformal Laplacians defined via the AHE manifold, we can define a fractional Yamabe problem, looking for a conformal metric of $(M^n,[\\hat{g}])$ which has constant fractional scalar curvature. We will present some new developments on the fractional Yamabe problem assuming an AHE filling in.<\/p>\n<p><strong>Venue:<\/strong> DIM seminar room, Beauchef 851, 5th floor.<\/p>\n<p><strong>Zoom:<\/strong> <a href=\"https:\/\/uchile.zoom.us\/j\/96642349167?pwd=MkRVbWxzOFBUUXlCTWFicW0reWZ6dz09\" target=\"_blank\" rel=\"noopener noreferrer\">https:\/\/uchile.zoom.us\/j\/96642349167?pwd=MkRVbWxzOFBUUXlCTWFicW0reWZ6dz09<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Sophie Aiken (University of California Santa Cruz)<\/p>\n","protected":false},"author":125,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[5],"tags":[],"class_list":["post-702","post","type-post","status-publish","format-standard","hentry","category-past-seminar"],"_links":{"self":[{"href":"https:\/\/eventos.cmm.uchile.cl\/pdeseminar\/wp-json\/wp\/v2\/posts\/702","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/eventos.cmm.uchile.cl\/pdeseminar\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/eventos.cmm.uchile.cl\/pdeseminar\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/eventos.cmm.uchile.cl\/pdeseminar\/wp-json\/wp\/v2\/users\/125"}],"replies":[{"embeddable":true,"href":"https:\/\/eventos.cmm.uchile.cl\/pdeseminar\/wp-json\/wp\/v2\/comments?post=702"}],"version-history":[{"count":1,"href":"https:\/\/eventos.cmm.uchile.cl\/pdeseminar\/wp-json\/wp\/v2\/posts\/702\/revisions"}],"predecessor-version":[{"id":703,"href":"https:\/\/eventos.cmm.uchile.cl\/pdeseminar\/wp-json\/wp\/v2\/posts\/702\/revisions\/703"}],"wp:attachment":[{"href":"https:\/\/eventos.cmm.uchile.cl\/pdeseminar\/wp-json\/wp\/v2\/media?parent=702"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/eventos.cmm.uchile.cl\/pdeseminar\/wp-json\/wp\/v2\/categories?post=702"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/eventos.cmm.uchile.cl\/pdeseminar\/wp-json\/wp\/v2\/tags?post=702"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}