{"id":1082,"date":"2016-10-21T12:42:24","date_gmt":"2016-10-21T16:42:24","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/boyland\/?page_id=1082"},"modified":"2026-03-19T08:10:28","modified_gmt":"2026-03-19T12:10:28","slug":"ezra-miller","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/boyland\/ezra-miller\/","title":{"rendered":"Ezra Miller"},"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\">Ezra Miller<\/h1>\n\n\n\n<h4 class=\"wp-block-heading\">Algebraic data structures for topological summaries<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Abstract:<br>\nThis talk introduces a combinatorial algebraic framework to encode,<br>\ncompute, and analyze topological summaries of geometric data.\u00a0 The<br>\nmotivating problem from evolutionary biology involves statistics on<br>\na dataset comprising images of fruit fly wing veins.\u00a0 The algebraic<br>\nstructures take their cue from graded polynomial rings and their<br>\nmodules, but the theory is complicated by the passage from integer<br>\nexponent vectors to real exponent vectors.\u00a0 The path to effective<br>\nmethods is built on appropriate finiteness conditions, to replace the<br>\nusual ones from commutative algebra, and on an understanding of how<br>\ndatasets of this nature interact with moduli of modules.\u00a0 I will<br>\nintroduce the biology, algebra, and topology from first principles.<br>\nJoint work with David Houle (Biology, Florida State), Ashleigh Thomas<br>\n(grad student, Duke Math), and Justin Curry (postdoc, Duke Math).<\/p>\n\n\n\n\n\n\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-1082","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/1082","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=1082"}],"version-history":[{"count":2,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/1082\/revisions"}],"predecessor-version":[{"id":4002,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/1082\/revisions\/4002"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/media?parent=1082"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}