{"id":424,"date":"2024-09-19T22:01:47","date_gmt":"2024-09-19T22:01:47","guid":{"rendered":"https:\/\/as.vanderbilt.edu\/newmath2025\/?p=424"},"modified":"2025-03-11T20:53:49","modified_gmt":"2025-03-11T20:53:49","slug":"september-19-2024-amenability-optimal-transport-and-abstract-ergodic-theorems","status":"publish","type":"post","link":"https:\/\/as.vanderbilt.edu\/math\/2024\/09\/19\/september-19-2024-amenability-optimal-transport-and-abstract-ergodic-theorems\/","title":{"rendered":"Colloquium &#8211; Amenability, optimal transport and abstract ergodic theorems : September 19, 2024"},"content":{"rendered":"<p><strong>September 19, 2024 (Thursday), 4:10 pm<\/strong><\/p>\n<div class=\"entry-summary\">\n<p>Christian Rosendal, University of Maryland<\/p>\n<p>The concept of amenability is ubiquitous in functional analysis, group theory and logic. In general, amenability of, for example, a group allows one to integrate bounded real valued functions on the group in a translation invariant manner, which is of great utility in many contexts. However, unbounded functions are a completely different matter. Nevertheless, by using tools from the theory of optimal transport, more specifically, optimal transportation cost spaces, we shall present a couple of results that show how one may integrate potentially unbounded Lipschitz functions defined on amenable groups as long as the latter admit no non-trivial homomorphism to $\\mathbb R$. This is related to previous results of Schneider\u2013Thom and Cuth\u2013Doucha in the bounded setting. The talk will be aimed at a general mathematical audience.<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>September 19, 2024 (Thursday), 4:10 pm Christian Rosendal, University of Maryland The concept of amenability is ubiquitous in functional analysis, group theory and logic. In general, amenability of, for example, a group allows one to integrate bounded real valued functions on the group in a translation invariant manner, which is of great utility in many&#8230;<\/p>\n","protected":false},"author":74,"featured_media":754,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[7],"tags":[],"acf":[],"jetpack_featured_media_url":"https:\/\/as.vanderbilt.edu\/math\/wp-content\/uploads\/sites\/69\/2024\/08\/colloquium.png","_links":{"self":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/424"}],"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=424"}],"version-history":[{"count":2,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/424\/revisions"}],"predecessor-version":[{"id":669,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/424\/revisions\/669"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/media\/754"}],"wp:attachment":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/media?parent=424"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/categories?post=424"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/tags?post=424"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}