{"id":691,"date":"2025-02-19T18:24:40","date_gmt":"2025-02-19T18:24:40","guid":{"rendered":"https:\/\/as.vanderbilt.edu\/newmath2025\/?p=691"},"modified":"2025-04-17T15:12:25","modified_gmt":"2025-04-17T15:12:25","slug":"topology-and-group-theory-seminar-february-19-2025","status":"publish","type":"post","link":"https:\/\/as.vanderbilt.edu\/math\/2025\/02\/19\/topology-and-group-theory-seminar-february-19-2025\/","title":{"rendered":"Topology and Group Theory Seminar: February 19, 2025"},"content":{"rendered":"<p><strong>Speaker: <\/strong>Denis Osin\u00a0(Vanderbilt)<\/p>\n<p><strong>Title:<\/strong><strong>\u00a0<\/strong><em>Simple p-adic Lie groups with abelian Lie algebras<\/em><\/p>\n<p><strong>Abstract:<\/strong><strong>\u00a0<\/strong>For each prime\u00a0<em>p<\/em>\u00a0and each positive integer\u00a0<em>d<\/em>, we construct the first examples of second countable, topologically simple,\u00a0<em>p<\/em>-adic Lie groups of dimension\u00a0<em>d<\/em>\u00a0with abelian\u00a0Lie algebras. This answers a question asked by P.-E. Caprace and N. Monod. In my talk, I will survey the necessary background material and explain why this question is of fundamental importance in the theory of\u00a0<em>p<\/em>-adic Lie groups. Perhaps surprisingly, the proof of the main result makes use of small cancellation techniques in groups acting on hyperbolic spaces. Geometric ideas come into play through a general construction that associates a non-discrete, totally disconnected topological group with any discrete group satisfying a certain algebraic condition. The talk is based on joint work with P.-E. Caprace and A. Minasyan.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Speaker: Denis Osin\u00a0(Vanderbilt) Title:\u00a0Simple p-adic Lie groups with abelian Lie algebras Abstract:\u00a0For each prime\u00a0p\u00a0and each positive integer\u00a0d, we construct the first examples of second countable, topologically simple,\u00a0p-adic Lie groups of dimension\u00a0d\u00a0with abelian\u00a0Lie algebras. This answers a question asked by P.-E. Caprace and N. Monod. In my talk, I will survey the necessary background material and&#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\/691"}],"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=691"}],"version-history":[{"count":1,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/691\/revisions"}],"predecessor-version":[{"id":737,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/691\/revisions\/737"}],"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=691"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/categories?post=691"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/tags?post=691"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}