The notion of Borel reducibility, developed mainly by
descriptive set theorists, is a tool for measuring the complexity of an
equivalence relation. Given a class of mathematical objects, it can
usually be applied to study the isomorphism relation between those
objects. In 2011, Foreman, Rudolph and Weiss showed that the conjugacy
of of ergodic MPS (measure-preserving systems) is not Borel. The result
can be interpreted as proof of non-existence of certain simpler
descriptions of when two ergodic MPS are isomorphic (for example, no
complete invariant exists). Several other classes of topological and
measurable dynamical systems have also been studied in a similar manner.
We will provide an introduction to the topic of Borel reducibility,
survey the results related to dynamical systems, and discuss some new
results.

Meeting ID: 852 4277 3200
Passcode: 103121