{"id":634,"date":"2025-02-28T23:19:15","date_gmt":"2025-02-28T23:19:15","guid":{"rendered":"https:\/\/as.vanderbilt.edu\/newmath2025\/?p=634"},"modified":"2025-04-17T15:12:25","modified_gmt":"2025-04-17T15:12:25","slug":"geometry-and-topology-seminar-friday-february-28th","status":"publish","type":"post","link":"https:\/\/as.vanderbilt.edu\/math\/2025\/02\/28\/geometry-and-topology-seminar-friday-february-28th\/","title":{"rendered":"Geometry and Topology Seminar: February 28, 2025"},"content":{"rendered":"<p><strong>Speaker<\/strong>:\u00a0Zhonghui Sun\u00a0(Michigan State University)<\/p>\n<p><strong>Title<\/strong>:\u00a0Equivariant Bicategorical Shadows and Traces<\/p>\n<p><strong>Abstract<\/strong>:\u00a0\u00a0Bicategorical shadows, defined by Ponto, provide a framework that generalizes (topological) Hochschild homology.\u00a0 Bicategorical shadows have important properties, such as Morita invariance, and allow one to generalize the symmetric monoidal trace to a bicategorical trace. Topological Hochschild homology (THH), an essential component<br \/>\nof the trace methods approach for algebraic K-theory, is a key example of a bicategorical shadow.<\/p>\n<p>In recent years, equivariant versions of topological Hochschild homology have emerged. In particular, for a C_n-ring spectrum, there is a theory of C_n-twisted THH, constructed via equivariant norms. However, twisted THH fails to be a bicategorical shadow. In this talk, we will explain a new framework of equivariant bicategorical shadows and explain why twisted THH is a g-twisted shadow. We also explore g-twisted bicategorical traces.<\/p>\n<p><strong>Contact<\/strong>: <a href=\"mailto:hannah.housden@vanderbilt.edu\">Hannah Housden<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Speaker:\u00a0Zhonghui Sun\u00a0(Michigan State University) Title:\u00a0Equivariant Bicategorical Shadows and Traces Abstract:\u00a0\u00a0Bicategorical shadows, defined by Ponto, provide a framework that generalizes (topological) Hochschild homology.\u00a0 Bicategorical shadows have important properties, such as Morita invariance, and allow one to generalize the symmetric monoidal trace to a bicategorical trace. Topological Hochschild homology (THH), an essential component of the trace methods&#8230;<\/p>\n","protected":false},"author":74,"featured_media":751,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[9],"tags":[],"acf":[],"jetpack_featured_media_url":"https:\/\/as.vanderbilt.edu\/math\/wp-content\/uploads\/sites\/69\/2025\/03\/geometry-topology.png","_links":{"self":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/634"}],"collection":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/users\/74"}],"replies":[{"embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/comments?post=634"}],"version-history":[{"count":2,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/634\/revisions"}],"predecessor-version":[{"id":661,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/634\/revisions\/661"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/media\/751"}],"wp:attachment":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/media?parent=634"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/categories?post=634"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/tags?post=634"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}