{"id":190,"date":"2025-08-08T13:23:50","date_gmt":"2025-08-08T17:23:50","guid":{"rendered":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/?p=190"},"modified":"2025-09-10T09:30:15","modified_gmt":"2025-09-10T12:30:15","slug":"inverse-scattering-for-asymptotically-hyperbolic-manifolds","status":"publish","type":"post","link":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/2025\/08\/inverse-scattering-for-asymptotically-hyperbolic-manifolds\/","title":{"rendered":"Inverse scattering for asymptotically hyperbolic manifolds"},"content":{"rendered":"<p><b class=\"\"><span class=\"\">D\u00cdA \/ HORA: <\/span><\/b><span class=\"\">Jueves 14 de agosto de 2025 \/ 14:30 &#8211; 15:30<\/span><\/p>\n<p><strong>EXPOSITOR:\u00a0Sebasti\u00e1n Mu\u00f1oz-Thon<\/strong>, Purdue University and Universit\u00e9 Paris-Saclay.<\/p>\n<div class=\"\">\n<p><b class=\"\"><span class=\"\">RESUMEN<\/span><\/b><span class=\"\">:<\/span>\u00a0On compact Riemannian manifolds with boundary, the (anisotropic) Calder\u00f3n&#8217;s problem asks to what extent the\u00a0Dirichlet-to-Neumann map associated with the Laplace\u2014Beltrami equation determines the metric (up to a natural obstruction).\u00a0In this talk, I will discuss a similar problem, known as inverse scattering for asymptotically hyperbolic manifolds (i.e., manifolds\u00a0that, outside a compact region, behave like the hyperbolic space): fixed an \u00abenergy level\u00bb, and \u00a0given the analog of the\u00a0Neumann data for solutions to certain 0-elliptic PDE depending on the fixed energy level, determine the metric of the manifold.\u00a0I will show that, under some geometric conditions, one can determine the Taylor series of the metric at the boundary.\u00a0The proof is based on the relation between this problem and the Calder\u00f3n problem for the Conformal Laplacian.<\/p>\n<\/div>\n<p><span class=\"\"><b class=\"\">IDIOMA: <\/b>Espa\u00f1ol<\/span><\/p>\n<div class=\"\">\n<p><b class=\"\"><span class=\"\">LUGAR<\/span><\/b><span class=\"\">: <\/span>Sala de Seminarios\u00a0Felipe Alvarez Daziano, 5to PISO,\u00a0Departamento de Ingenier\u00eda Matem\u00e1tica,\u00a0FCFM\u00a0Universidad de Chile.<\/p>\n<div class=\"\"><span class=\"\"><strong>DIRECCI\u00d3N: <\/strong>Av. Beauchef 851, Santiago, Chile. <\/span><span class=\"\"><a href=\"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/lugar\/\">C\u00f3mo llegar<\/a>.<\/span><\/div>\n<\/div>\n<div><\/div>\n<div class=\"\"><strong>MODALIDAD:<\/strong> Presencial y transmisi\u00f3n por Zoom. Link aqu\u00ed: <a href=\"https:\/\/uchile.zoom.us\/j\/92044916826?pwd=ej2BCvabntOIuSXsN6abvAMzJSFzPP.1\">ZOOM<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Sebasti\u00e1n Mu\u00f1oz-Thon, Purdue University and Universit\u00e9 Paris-Saclay<\/p>\n","protected":false},"author":116,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[],"class_list":["post-190","post","type-post","status-publish","format-standard","hentry","category-seminarios"],"_links":{"self":[{"href":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/wp-json\/wp\/v2\/posts\/190","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/wp-json\/wp\/v2\/users\/116"}],"replies":[{"embeddable":true,"href":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/wp-json\/wp\/v2\/comments?post=190"}],"version-history":[{"count":4,"href":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/wp-json\/wp\/v2\/posts\/190\/revisions"}],"predecessor-version":[{"id":207,"href":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/wp-json\/wp\/v2\/posts\/190\/revisions\/207"}],"wp:attachment":[{"href":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/wp-json\/wp\/v2\/media?parent=190"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/wp-json\/wp\/v2\/categories?post=190"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/wp-json\/wp\/v2\/tags?post=190"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}