{"id":109,"date":"2022-06-22T11:14:58","date_gmt":"2022-06-22T15:14:58","guid":{"rendered":"https:\/\/sites.nd.edu\/mgsa\/?page_id=109"},"modified":"2025-12-12T13:20:16","modified_gmt":"2025-12-12T18:20:16","slug":"summer-2021","status":"publish","type":"page","link":"https:\/\/sites.nd.edu\/mgsa\/graduate-student-seminar\/summer-2021\/","title":{"rendered":"Summer 2021"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\">7\/12\/2021 &#8211; Randy Van Why (Northwestern): Disk bundle plumbings, lens spaces, and continued fractions<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">I will attempt to state and prove a theorem showing a strange connection between continued fractions, lens spaces, and disk bundle plumbings. I will start by introducing the plumbing construction and surgery and then sketch a proof of the theorem.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">6\/14\/2021 &#8211; Hari Rau-Murthy: The matrix exponential, the Bismut Chern character, and the character of a representation<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The matrix exponential can be used to solve the differential equation d\u03b3\/dt = A(t)\u03b3(t)$. We will discuss a cool trick involving this matrix exponential. This trick will be used to define the Bismut Chern character, which is the trace of a certain matrix exponential associated to a loop, \u03b3(t), in a manifold. The Bismut Chern character has striking connections to the group theoretic character of a representation, which is trace of a matrix that represents an element, g, of a group. The loop \u03b3(t) will end up corresponding to the conjugacy class of g. Thus we relate a differential geometric construction to an algebraic construction.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>7\/12\/2021 &#8211; Randy Van Why (Northwestern): Disk bundle plumbings, lens spaces, and continued fractions I will attempt to state and prove a theorem showing a strange connection between continued fractions, lens spaces, and disk bundle plumbings. I will start by introducing the plumbing construction and surgery and then sketch a proof of the theorem. 6\/14\/2021 [&hellip;]<\/p>\n","protected":false},"author":2271,"featured_media":0,"parent":55,"menu_order":9,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-109","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sites.nd.edu\/mgsa\/wp-json\/wp\/v2\/pages\/109","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.nd.edu\/mgsa\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.nd.edu\/mgsa\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.nd.edu\/mgsa\/wp-json\/wp\/v2\/users\/2271"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.nd.edu\/mgsa\/wp-json\/wp\/v2\/comments?post=109"}],"version-history":[{"count":3,"href":"https:\/\/sites.nd.edu\/mgsa\/wp-json\/wp\/v2\/pages\/109\/revisions"}],"predecessor-version":[{"id":122,"href":"https:\/\/sites.nd.edu\/mgsa\/wp-json\/wp\/v2\/pages\/109\/revisions\/122"}],"up":[{"embeddable":true,"href":"https:\/\/sites.nd.edu\/mgsa\/wp-json\/wp\/v2\/pages\/55"}],"wp:attachment":[{"href":"https:\/\/sites.nd.edu\/mgsa\/wp-json\/wp\/v2\/media?parent=109"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}