{"id":3520,"date":"2023-01-11T13:41:53","date_gmt":"2023-01-11T18:41:53","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/boyland\/?page_id=3520"},"modified":"2026-03-19T08:10:24","modified_gmt":"2026-03-19T12:10:24","slug":"anna-e-weigandt","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/boyland\/anna-e-weigandt\/","title":{"rendered":"Anna E Weigandt"},"content":{"rendered":"\r\n<section class=\"fullwidth-text-block\">\r\n\t<div class=\"container px-0 pt-5\">\r\n\t\t<div class=\"row align-items-start\">\r\n\t\t\t<div class=\"col-12\">\r\n\t\t\t\t\n<h1 class=\"wp-block-heading\">Anna E Weigandt<\/h1>\n\n\n\n<h3 class=\"wp-block-heading\">Combinatorial Aspects of Determinantal Varieties<\/h3>\n\n\n\n<p>Abstract: Schubert calculus has its origins in enumerative questions asked by the geometers of the 19th century, such as &#8220;how many lines meet four fixed lines in three-space?&#8221;\u00a0 These problems can be recast as questions about the structure of cohomology rings of geometric spaces such as flag varieties.\u00a0 Borel&#8217;s isomorphism identifies the cohomology of the complete flag variety with a simple quotient of a polynomial ring.\u00a0 Lascoux and Sch\u00fctzenberger (1982) defined Schubert polynomials, which are coset representatives for the Schubert basis of this ring. However, it was not clear if this choice was geometrically natural.\u00a0 Knutson and Miller (2005) provided a justification for the naturality of Schubert polynomials via antidiagonal Gr\u00f6bner degenerations of matrix Schubert varieties, which are generalized determinantal varieties. Furthermore, they showed that pre-existing combinatorial objects called pipe dreams govern this degeneration.\u00a0 In this talk, we study the dual setting of diagonal Gr\u00f6bner degenerations of matrix Schubert varieties, interpreting these limits in terms of the &#8220;bumpless pipe dreams&#8221; of Lam, Lee, and Shimozono (2021).\u00a0 We then use the combinatorics of K-theory representatives for Schubert classes to compute the Castelnuovo-Mumford regularity of matrix Schubert varieties, which gives a bound on the complexity of their coordinate rings.<\/p>\n\n\n\n\n\n\n\n\n\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t<\/div>\r\n<\/section>\r\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":146,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-3520","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/3520","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/users\/146"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/comments?post=3520"}],"version-history":[{"count":2,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/3520\/revisions"}],"predecessor-version":[{"id":3817,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/3520\/revisions\/3817"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/media?parent=3520"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}