{"id":586,"date":"2023-02-12T16:30:22","date_gmt":"2023-02-13T00:30:22","guid":{"rendered":"\/wp\/hades\/?p=586"},"modified":"2023-02-12T16:30:22","modified_gmt":"2023-02-13T00:30:22","slug":"the-tensorial-x-ray-transform-on-asymptotically-conic-manifolds","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2023\/02\/12\/the-tensorial-x-ray-transform-on-asymptotically-conic-manifolds\/","title":{"rendered":"The Tensorial X-ray Transform on Asymptotically Conic Manifolds"},"content":{"rendered":"\n\t\t\t\t\n<p class=\"wp-block-paragraph\"> The HADES seminar on Tuesday, <strong>March 14th<\/strong>\u00a0will be at\u00a0<strong>3:30 pm<\/strong>\u00a0in\u00a0<strong>Room 740<\/strong>.  <\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Speaker:<\/strong> Qiuye Jia<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Abstract:<\/strong> In this talk I will discuss the invertibility of the geodesic X-ray<br>\ntransform on one forms and 2-tensors on asymptotically conic<br>\nmanifolds, up to the natural obstruction, allowing existence of<br>\ncertain kinds of conjugate points. We use the 1-cusp<br>\npseudodifferential operator algebra and its semiclassical foliation<br>\nversion introduced and used by Vasy and Zachos, who showed the same type<br>\ninvertibility on functions.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The complication of the invertibility of the tensorial X-ray<br>\ntransform, compared with X-ray transform on functions, is caused by<br>\nthe natural kernel of the transform consisting of `potential<br>\ntensors&#8217;. We overcome this by arranging a modified solenoidal gauge condition, <br>\nunder which we have the invertibility of the X-ray transform.<\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday, March 14th\u00a0will be at\u00a03:30 pm\u00a0in\u00a0Room 740. Speaker: Qiuye Jia Abstract: In this talk I will discuss the invertibility of the geodesic X-ray transform on one forms and 2-tensors on asymptotically conic manifolds, up to the natural obstruction, allowing existence of certain kinds of conjugate points. We use the 1-cusp pseudodifferential [&hellip;]<\/p>\n","protected":false},"author":88,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-586","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/586","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/users\/88"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=586"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/586\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=586"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=586"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=586"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}