"Non UBC"@en .
"DSpace"@en .
"Dominik Kwietniak"@en .
"2019-11-11T10:23:47Z"@en .
"2019-05-14T16:30"@en .
"Rufus Bowen left a notebook containing 157 open problems and\nquestions. Problem 32 on that list asks for classification of shift\nspaces with the specification property. Unfortunately, there is no\nuniversally accepted agreement what does it mean \u00C3\u00A2to classify\u00C3\u00A2 a\nfamily of mathematical objects, and Bowen didn't left any clues.\nDuring my talk, I will describe one of the most popular ways of making\nthe problem formal. It is based on the theory of Borel equivalence\nrelations. Inside that framework, I will explain a result saying that\n(roughly speaking) there is no reasonable classification for shift\nspaces with the specification property. More precisely, I will show\nthat the isomorphism relation on the space of shifts with the\nspecification property is a universal countable Borel equivalence\nrelation, i.e. for every countable Borel equivalence relation $F$, we\nhave that $F$ is Borel reducible to $E$. It follows that no classification\nusing a finite set of definable invariants is possible. This solves\nthe problem provided that Bowen would agree with the notion of\n\u00C3\u00A2classification\u00C3\u00A2 provided by the theory of Borel equivalence\nrelations."@en .
"https://circle.library.ubc.ca/rest/handle/2429/72248?expand=metadata"@en .
"50.0 minutes"@en .
"video/mp4"@en .
""@en .
"Author affiliation: Jagiellonian University"@en .
"Oaxaca (Mexico : State)"@en .
"10.14288/1.0385160"@en .
"eng"@en .
"Unreviewed"@en .
"Vancouver : University of British Columbia Library"@en .
"Banff International Research Station for Mathematical Innovation and Discovery"@en .
"Attribution-NonCommercial-NoDerivatives 4.0 International"@en .
"http://creativecommons.org/licenses/by-nc-nd/4.0/"@en .
"Researcher"@en .
"BIRS Workshop Lecture Videos (Oaxaca (Mexico : State))"@en .
"Mathematics"@en .
"Dynamical Systems And Ergodic Theory, Group Theory And Generalizations, Dynamical Systems"@en .
"On Problem 32 from Rufus Bowen's list: classification of shift spaces with specification"@en .
"Moving Image"@en .
"http://hdl.handle.net/2429/72248"@en .