{"id":230,"date":"2024-02-26T18:25:05","date_gmt":"2024-02-26T16:25:05","guid":{"rendered":"https:\/\/mat.uab.cat\/web\/gentle\/?p=230"},"modified":"2024-03-08T17:25:02","modified_gmt":"2024-03-08T15:25:02","slug":"courant-cohomology-cartan-calculus-connections-curvature-characteristic-classes-by-m-cueca","status":"publish","type":"post","link":"https:\/\/mat.uab.cat\/web\/gentle\/2024\/02\/26\/courant-cohomology-cartan-calculus-connections-curvature-characteristic-classes-by-m-cueca\/","title":{"rendered":"Courant cohomology, Cartan calculus, connections, curvature, characteristic classes, by M. Cueca"},"content":{"rendered":"<p>7 Mar 2024, 11h CET. Talk by M. Cueca.<\/p>\n<p>Abstract: It is known that Courant algebroids are in correspondence with degree 2 symplectic dg-manifolds. The standard cochain complex of a Courant algebroid is, by definition, the complex consisting of functions on the corresponding dg-manifold. This definition has been difficult to work with directly, due to a lack of explicit ordinate-free formulas relating the Courant data (bracket, anchor, and pairing) to the standard complex. In this talk, I will give a description of the standard complex in terms of the Courant data, and I will explain how the differential satisfies a familiar-looking Cartan formula. As an application, I will explain how the classical theory of connections extends almost verbatim to Courant algebroids, leading to a construction of secondary characteristic classes that formally resembles the classical Chern-Simons construction. This is joint work with Rajan Mehta.<\/p>\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/mat.uab.cat\/web\/gentle\/wp-content\/uploads\/sites\/38\/2024\/03\/Beamer_Presentation6.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Incrustaci\u00f3 del fitxer Slides:.\"><\/object><a id=\"wp-block-file--media-71e862c3-bf2e-4524-9a94-4bdfb5314e3f\" href=\"https:\/\/mat.uab.cat\/web\/gentle\/wp-content\/uploads\/sites\/38\/2024\/03\/Beamer_Presentation6.pdf\">Slides:<\/a><a href=\"https:\/\/mat.uab.cat\/web\/gentle\/wp-content\/uploads\/sites\/38\/2024\/03\/Beamer_Presentation6.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-71e862c3-bf2e-4524-9a94-4bdfb5314e3f\">Download<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>7 Mar 2024, 11h CET. Talk by M. Cueca. Abstract: It is known that Courant algebroids are in correspondence with degree 2 symplectic dg-manifolds. The standard cochain complex of a Courant algebroid is, by definition, the complex consisting of functions on the corresponding dg-manifold. This definition has been difficult to work with directly, due to [&hellip;]<\/p>\n","protected":false},"author":54,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[40],"tags":[],"class_list":["post-230","post","type-post","status-publish","format-standard","hentry","category-2023-2024"],"_links":{"self":[{"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/posts\/230","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/users\/54"}],"replies":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/comments?post=230"}],"version-history":[{"count":5,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/posts\/230\/revisions"}],"predecessor-version":[{"id":269,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/posts\/230\/revisions\/269"}],"wp:attachment":[{"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/media?parent=230"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/categories?post=230"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/tags?post=230"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}