Logic Seminar
Matt Foreman
UCI
Classifying the qualitative behavior of smooth transformations using descriptive set theory
Abstract: In 1967 Smale proposed classifying the "qualitative behavior” of diffeomorphisms of compact smooth manifolds. Despite very significant activity, the general problem remained open. However joint work with Gorodetski shows that in dimensions 2 and above, there are no complete invariants and in dimension 5 and above the equivalence relation is not even Borel. Hence there can be no classification using inherently countable information.
Tuesday March 15, 2022 at 4:00 PM in 636 SEO