{"id":738,"date":"2025-02-12T18:25:25","date_gmt":"2025-02-12T18:25:25","guid":{"rendered":"https:\/\/as.vanderbilt.edu\/newmath2025\/?p=738"},"modified":"2025-04-17T15:12:25","modified_gmt":"2025-04-17T15:12:25","slug":"topology-and-group-theory-seminar-february-12-2025","status":"publish","type":"post","link":"https:\/\/as.vanderbilt.edu\/math\/2025\/02\/12\/topology-and-group-theory-seminar-february-12-2025\/","title":{"rendered":"Topology and Group Theory Seminar: February 12, 2025"},"content":{"rendered":"<p><strong>Speaker: <\/strong>Jesse Peterson (Vanderbilt)<\/p>\n<p><strong>Title:<\/strong><strong>\u00a0<\/strong><em>Property HaHaHaHaHaHaHaHaHaHaHa\u2026 HaHaHaHaHaHaHaHaHa\u2026 HaHaHaHaHaHa\u2026 HaHaHa\u2026<\/em><em>\u00a0<\/em><\/p>\n<p><strong>Abstract:<\/strong><strong>\u00a0<\/strong>A seminal result of Haagerup from 1979 is that the word length function with respect to a free generating set on a free group is conditionally negative definite. Groups possessing a proper conditionally negative definite function have since been said to have the Haagerup property and comprise a large and well-studied class of groups containing all amenable groups in addition to free groups. The Haagerup property is a particularly nice analytic approximation property since it passes to subgroups, is a local property, and is stable under measure-equivalence and\u00a0<em>W*<\/em>-equivalence. One drawback however is that it is not in general closed under extensions. In this talk, I will discuss a weakening of the Haagerup property, which still has many nice analytic properties, but is more flexible when it comes to constructions such as group extensions. In fact, I will discuss a hierarchy of such properties indexed by the countable ordinals. This is joint work with Fabian Salinas.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Speaker: Jesse Peterson (Vanderbilt) Title:\u00a0Property HaHaHaHaHaHaHaHaHaHaHa\u2026 HaHaHaHaHaHaHaHaHa\u2026 HaHaHaHaHaHa\u2026 HaHaHa\u2026\u00a0 Abstract:\u00a0A seminal result of Haagerup from 1979 is that the word length function with respect to a free generating set on a free group is conditionally negative definite. Groups possessing a proper conditionally negative definite function have since been said to have the Haagerup property 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\/738"}],"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=738"}],"version-history":[{"count":1,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/738\/revisions"}],"predecessor-version":[{"id":739,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/738\/revisions\/739"}],"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=738"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/categories?post=738"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/tags?post=738"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}