{"id":466,"date":"2020-01-15T11:51:13","date_gmt":"2020-01-15T11:51:13","guid":{"rendered":"http:\/\/blogs.kent.ac.uk\/pgrseminars\/?p=466"},"modified":"2020-01-15T11:52:56","modified_gmt":"2020-01-15T11:52:56","slug":"friezes-and-cluster-algebras-joe","status":"publish","type":"post","link":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/2020\/01\/15\/friezes-and-cluster-algebras-joe\/","title":{"rendered":"Friezes and cluster algebras (Joe Pallister)"},"content":{"rendered":"<p class=\"lead\">16:00, January 17, Kennedy Seminar Room 2<\/p>\n<p><strong>Abstract<\/strong>:\u00a0\u00a0&#8220;A Coxeter-Conway frieze is a planar array of integers, bounded above and below by rows of ones, such that every neighbouring set of 4 entries satisfies an SL_2 determinant condition. We discuss elementary results about friezes including a bijection between them and triangulations of n-gons.<\/p>\n<p>Cluster algebras are algebras whose (possible infinite) set of generators is constructed algorithmically, starting from an initial set of cluster variables and a quiver, whose combinatorics give the relations between the newly constructed variables. We discuss how one may obtain dynamical systems from cluster algebras and how friezes are obtained from a special set of cluster algebras.&#8221;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>16:00, January 17, Kennedy Seminar Room 2 Abstract:\u00a0\u00a0&#8220;A Coxeter-Conway frieze is a planar array of integers, bounded above and below by rows of ones, such &hellip; <a href=\"https:\/\/blogs.kent.ac.uk\/pgrseminars\/2020\/01\/15\/friezes-and-cluster-algebras-joe\/\">Read&nbsp;more<\/a><\/p>\n","protected":false},"author":64811,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[208120],"tags":[],"_links":{"self":[{"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/posts\/466"}],"collection":[{"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/users\/64811"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/comments?post=466"}],"version-history":[{"count":2,"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/posts\/466\/revisions"}],"predecessor-version":[{"id":468,"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/posts\/466\/revisions\/468"}],"wp:attachment":[{"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/media?parent=466"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/categories?post=466"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/tags?post=466"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}