Speaker: AARON HILL (University of North Texas)

Title: The Topological Isomorphism Problem for Rank-1 Systems (part 1)

Abstract: In a 2011 paper, Foreman, Rudolph, and Weiss showed that while the isomorphism relation on ergodic measure-preserving transformations is complete analytic, it is Borel when restricted to the class of rank-1 transformations. However, there is no explicit description of when two rank-1 transformations are isomorphic. In this talk we discuss the Polish space of concrete rank-1 systems. Each concrete rank-1 system is a measure-preserving transformation of a standard Lebesgue space and a homeomorphism of Cantor space. We prove that the topological isomorphism relation on the space of concrete rank-1 systems is Borel and we'll give an explicit description of when two concrete rank-1 systems are topologically isomorphic. We'll also show that the topological isomorphism relation on concrete rank-1 systems is bi-reducible to E_0.