# The isomorphism problem for rank-1 transformations

## Aaron Hill

### University of Louisville

I’ll begin by describing two fascinating questions in ergodic theory, one being the isomorphism problem for measure-preserving transformations. I’ll survey some of the progress that has been made on these problems, including some partial solutions to the isomorphism problem for certain classes of measure-preserving transformations and some anti-classification results, stating that “nice” solutions to the isomorphism problem are impossible on other classes of measure-preserving transformations. Then I’ll discuss recent work I’ve done with Su Gao on the isomorphism problem for the class of rank-1 transformations, a generic class of measure-preserving transformations where the isomorphism relation is known to be, in some sense, well-behaved. (Background information ergodic theory will be introduced as needed.)

Dr. Aaron Hill is an assistant professor at the University of Louisville. He received his PhD from the University of Illinois at Urbana-Champaign under the supervision of Slawomir Solecki in 2011 and has held a postdoctoral position at the University of North Texas. His research interests include descriptive set theory, ergodic theory, and topological dynamics.