{"id":997,"date":"2016-03-02T20:58:22","date_gmt":"2016-03-03T01:58:22","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/boyland\/?page_id=997"},"modified":"2026-03-19T08:10:28","modified_gmt":"2026-03-19T12:10:28","slug":"matthew-kahle","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/boyland\/matthew-kahle\/","title":{"rendered":"Matthew Kahle"},"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\">Matthew Kahle<\/h1>\n\n\n\n<p>Title: Recent progress in stochastic topology<br class=\"\"> <br class=\"\"> Abstract: (This talk is intended for a broad audience, and no<br class=\"\"> particular prerequisite knowledge about topology or probability will<br class=\"\"> be assumed.) The study of random topological spaces: manifolds,<br class=\"\"> simplicial complexes, knots, and groups, has received a lot of<br class=\"\"> attention in recent years. This talk will mostly focus on random<br class=\"\"> simplicial complexes, and especially on a certain kind of topological<br class=\"\"> phase transition, where the probability that that a certain homology<br class=\"\"> group is trivial passes from 0 to 1 within a narrow window. The<br class=\"\"> archetypal result in this area is the Erd\u0151s\u2013R\u00e9nyi theorem, which<br class=\"\"> characterizes the threshold edge probability where the random graph<br class=\"\"> becomes connected. One recent breakthrough has been in the application<br class=\"\"> of Garland\u2019s method, which allows one to prove homology-vanishing<br class=\"\"> theorems by showing that certain Laplacians have large spectral gaps.<br class=\"\"> This reduces certain problems in stochastic topology to understanding<br class=\"\"> eigenvalues of certain random matrices, and the method has been<br class=\"\"> surprisingly successful. This is joint work with Christopher Hoffman<br class=\"\"> and Elliot Paquette.<\/p>\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-997","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/997","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=997"}],"version-history":[{"count":3,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/997\/revisions"}],"predecessor-version":[{"id":4011,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/997\/revisions\/4011"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/media?parent=997"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}