Special Colloquium
Christian Rosendal
University of Illinois at Urbana-Champaign
Descriptive Kakutani equivalence
Abstract: A very active part of modern descriptive set theory concerns the deep interactions with dynamical systems and ergodic theory. In particular, during the last 20 years the study of Borel measurable
equivalence relations and the ways of generating these have received extensive treatment, paralleling some of the theory of equivalence relations in the ergodic context, but also showing very different phenomena in other cases.
Of special interest are the equivalence relations generated by a single automorphism that have been fully classified up to orbit equivalence by Dougherty, Jackson and Kechris. On the other hand, Borel automorphisms themselves have been shown to be essentially unclassifiable up to conjugacy by Clemens.
We consider a decriptive analogue of Kakutani equivalence, which is motivated by a classical problem of Poincare on the structure of flows up to a time change, and show that there are exactly two Kakutani equivalence classes of Borel automorphisms. This is joint work with Benjamin D. Miller.
There will be a meet and greet right after the talk in SEO 300. Coffee, tea, & cookies will be provided.
Wednesday January 30, 2008 at 3:00 PM in SEO 636