{"id":742,"date":"2025-01-29T18:26:21","date_gmt":"2025-01-29T18:26:21","guid":{"rendered":"https:\/\/as.vanderbilt.edu\/newmath2025\/?p=742"},"modified":"2025-04-17T15:12:25","modified_gmt":"2025-04-17T15:12:25","slug":"topology-and-group-theory-seminar-january-29-2025","status":"publish","type":"post","link":"https:\/\/as.vanderbilt.edu\/math\/2025\/01\/29\/topology-and-group-theory-seminar-january-29-2025\/","title":{"rendered":"Topology and Group Theory Seminar: January 29, 2025"},"content":{"rendered":"<p><strong>Speaker:<\/strong> Abdul Zalloum\u00a0(University of Toronto)<\/p>\n<p><strong>Title:<\/strong><strong>\u00a0<\/strong><em>From<\/em><em>\u00a0<\/em><em>coarse to<\/em><em>\u00a0<\/em><em>fine:<\/em><em>\u00a0<\/em><em>a<\/em><em>\u00a0<\/em><em>generalized Sageev\u2019s<\/em><em>\u00a0<\/em><em>construction in<\/em><em>\u00a0<\/em><em>hyperbolic<\/em><em>\u00a0<\/em><em>spaces<\/em><\/p>\n<p><strong>Abstract:<\/strong><strong>\u00a0<\/strong>I will discuss a construction that starts with a set\u00a0<em>S<\/em>, a collection of bi-partitions on\u00a0<em>S<\/em>\u00a0called walls, and produces a spectrum of metric spaces, including Helly graphs, hyperbolic spaces, and injective metric spaces. The resulting space depends on the combinatorics of the walls; for example, if pairs of points are separated by finitely many walls, the resulting metric space is exactly Sageev\u2019s dual\u00a0<em>CAT(0)<\/em>\u00a0cube complex. I will also discuss a range of applications of this construction, with focus on the most recent: in joint work with Petyt-Spriano, we use the above framework to show that residually finite hyperbolic groups admit globally stable cylinders, addressing a question of Rips-Sela who asked in 1995 whether torsion-free hyperbolic groups possess such cylinders.<\/p>\n<p><strong>Host:<\/strong>\u00a0Dan Margalit<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Speaker: Abdul Zalloum\u00a0(University of Toronto) Title:\u00a0From\u00a0coarse to\u00a0fine:\u00a0a\u00a0generalized Sageev\u2019s\u00a0construction in\u00a0hyperbolic\u00a0spaces Abstract:\u00a0I will discuss a construction that starts with a set\u00a0S, a collection of bi-partitions on\u00a0S\u00a0called walls, and produces a spectrum of metric spaces, including Helly graphs, hyperbolic spaces, and injective metric spaces. The resulting space depends on the combinatorics of the walls; for example, if pairs&#8230;<\/p>\n","protected":false},"author":74,"featured_media":736,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[12],"tags":[],"acf":[],"jetpack_featured_media_url":"https:\/\/as.vanderbilt.edu\/math\/wp-content\/uploads\/sites\/69\/2025\/03\/topology-grouptheory.png","_links":{"self":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/742"}],"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=742"}],"version-history":[{"count":1,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/742\/revisions"}],"predecessor-version":[{"id":743,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/742\/revisions\/743"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/media\/736"}],"wp:attachment":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/media?parent=742"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/categories?post=742"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/tags?post=742"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}