{"id":2405,"date":"2022-05-29T13:09:15","date_gmt":"2022-05-29T10:09:15","guid":{"rendered":"https:\/\/mathematics.haifa.ac.il\/?p=2405"},"modified":"2022-06-05T11:42:05","modified_gmt":"2022-06-05T08:42:05","slug":"u-haifa-topology-geometry-seminar-sunday-may-29-2022-speaker-markus-upmeier-aberdeen-title-cobordism-categories-and-atiyah-singer-index-theory","status":"publish","type":"post","link":"https:\/\/mathematics.haifa.ac.il\/?p=2405","title":{"rendered":"U. Haifa Topology &#038; Geometry seminar: Sunday, May 29, 2022. Speaker: Markus Upmeier (Aberdeen). Title: &#8220;Cobordism categories and Atiyah-Singer index theory&#8221;."},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><strong>Time: <\/strong>17:00 (Israel Time)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Location: <\/strong>On Zoom<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Recording:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/us02web.zoom.us\/rec\/share\/OCd0OzhQnH8AcW2AjbpVGS5hFi4vW11OkS6gE0sFu7oVeakAviNsc0RJMB0BeneB.nQls_DORtJQrjgt3\">https:\/\/us02web.zoom.us\/rec\/share\/OCd0OzhQnH8AcW2AjbpVGS5hFi4vW11OkS6gE0sFu7oVeakAviNsc0RJMB0BeneB.nQls_DORtJQrjgt3<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Abstract.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp; I will discuss work in progress that categorifies the analytic index of Atiyah-Singer in terms of a new construction using&nbsp;representation theory of Clifford algebras. My main theorem shows that these new categorical indices can be organized into an&nbsp;invertible TQFT, in other words, a categorical group representation of the cobordism category.<br><br>The motivation for all this is that the construction of enumerative invariants requires a good understanding of differential-topological&nbsp;properties of moduli spaces, and the main theorem has applications to this. Important examples include instanton counting&nbsp;problems in gauge theory and algebraic geometry.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>ZOOM COORDINATES:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/us02web.zoom.us\/j\/84987591026?pwd=aTJWcFlOSldKck5leGt2d25CYkRqZz09\">https:\/\/us02web.zoom.us\/j\/84987591026?pwd=aTJWcFlOSldKck5leGt2d25CYkRqZz09<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Meeting ID: 849 8759 1026<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Future speakers:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Denis-Charles Cisinski (Regensburg) \u2013 June 5<sup>th<\/sup>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Time: 17:00 (Israel Time) Location: On Zoom Recording: https:\/\/us02web.zoom.us\/rec\/share\/OCd0OzhQnH8AcW2AjbpVGS5hFi4vW11OkS6gE0sFu7oVeakAviNsc0RJMB0BeneB.nQls_DORtJQrjgt3 Abstract. &nbsp; I will discuss work in progress that categorifies the analytic index of Atiyah-Singer in terms of a new construction using&nbsp;representation theory of Clifford algebras. My main theorem shows that&#8230;<br \/><a class=\"read-more-button\" href=\"https:\/\/mathematics.haifa.ac.il\/?p=2405\">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-2405","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\/2405","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=2405"}],"version-history":[{"count":4,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/2405\/revisions"}],"predecessor-version":[{"id":2409,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/2405\/revisions\/2409"}],"wp:attachment":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2405"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2405"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2405"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}