Impossibility results in ergodic theory and smooth dynamical systems

School of Mathematics Colloquium
Thursday, February 25, 2021 - 11:00am for 1 hour (actually 50 minutes)
Matthew Foreman – University of California, Irvine – mforeman@math.uci.edu
Anton Bernshteyn

The talk considers the equivalence relations of topological conjugacy and measure isomorphism on diffeomorphisms of compact manifolds of small dimension. It is shown that neither is a Borel equivalence relation.  As a consequence, there is no inherently countable method that,  for general diffeomorphisms $S$ and $T$, determines whether $S\sim T$. It is also shown that the Time Forward/Time Backward problem for diffeomorphisms of the 2-torus  encodes most mathematical questions, such as the Riemann Hypothesis.

This work is joint with B Weiss and A Gorodetski.