{"id":1565,"date":"2019-11-04T10:59:20","date_gmt":"2019-11-04T08:59:20","guid":{"rendered":"https:\/\/mathematics.haifa.ac.il\/?p=1565"},"modified":"2019-11-04T10:59:20","modified_gmt":"2019-11-04T08:59:20","slug":"this-week-thursday-at-1100-u-haifa-topology-geometry-seminar-on-november-7-2019","status":"publish","type":"post","link":"https:\/\/mathematics.haifa.ac.il\/?p=1565","title":{"rendered":"This week, Thursday at 11:00, U. Haifa Topology &#038; Geometry seminar on November 7, 2019"},"content":{"rendered":"<p style=\"font-weight: 400;\"><strong><u>Geometry\u00a0&amp; Topology Seminar<\/u><\/strong><\/p>\n<p style=\"font-weight: 400;\">\n<p style=\"font-weight: 400;\">Speaker:\u00a0Marina Prokhorova\u00a0(Technion)<\/p>\n<p style=\"font-weight: 400;\">\n<p style=\"font-weight: 400;\">Topic:\u00a0Family index for self-adjoint elliptic boundary value problems<\/p>\n<p style=\"font-weight: 400;\">Place:\u00a0 \u00a0 Room 614 in the Science &amp; Education Building<\/p>\n<p style=\"font-weight: 400;\">Time:\u00a0 \u00a011:00<\/p>\n<p style=\"font-weight: 400;\">Date:\u00a0 Thursday, November 7, 2019<\/p>\n<p style=\"font-weight: 400;\">\n<p style=\"font-weight: 400;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<strong><u>Abstract<\/u><\/strong><strong><u>:<\/u><\/strong><\/p>\n<p>An index theory for elliptic operators on a closed manifold was developed by Atiyah and Singer. For a family of such operators parametrized by points of a compact space X, they computed the K^0(X)-valued analytical index in purely topological terms. An analog of this theory for self-adjoint elliptic operators on closed manifolds was developed by Atiyah, Patodi, and Singer; the analytical index of a family in this case takes values in the K^1 group of a base space.<\/p>\n<p>If a manifold has non-empty boundary, then boundary conditions come into play, and situation becomes much more complicated. The integer-valued index of a single\u00a0boundary value problem\u00a0was computed by Boutet de Monvel. This result was recently generalized to K^0-valued family index by Melo, Schrohe, and Schick. The case of self-adjoint operators, however, remained open; it seems that Boutet de Monvel&#8217;s calculus is not adapted to it.<\/p>\n<p>In the talk I present a family index theorem for self-adjoint elliptic operators on a surface with boundary. I compute the K^1(X)-valued\u00a0analytical\u00a0index in terms of the topological data of the family over the boundary. The talk is based on my preprint arXiv:1809.04353.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Geometry\u00a0&amp; Topology Seminar Speaker:\u00a0Marina Prokhorova\u00a0(Technion) Topic:\u00a0Family index for self-adjoint elliptic boundary value problems Place:\u00a0 \u00a0 Room 614 in the Science &amp; Education Building Time:\u00a0 \u00a011:00 Date:\u00a0 Thursday, November 7, 2019 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Abstract: An index theory for elliptic operators on a closed&#8230;<br \/><a class=\"read-more-button\" href=\"https:\/\/mathematics.haifa.ac.il\/?p=1565\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6,4],"tags":[],"class_list":["post-1565","post","type-post","status-publish","format-standard","hentry","category-gt-seminar","category-seminar"],"_links":{"self":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/1565","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1565"}],"version-history":[{"count":1,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/1565\/revisions"}],"predecessor-version":[{"id":1566,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/1565\/revisions\/1566"}],"wp:attachment":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1565"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1565"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1565"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}