The Mackey-Zimmer representation theorem is a key structural result from ergodic theory: Every compact extension between ergodic measure-preserving systems can be written as a skew-product by a homogeneous space of a compact group. This is used, e.g., in Furstenberg’s original ergodic theoretic proof of Szemerédi’s theorem, as well as in the classical proofs of the Host-Kra-Ziegler structure theorem for characteristic factors. Inspired by earlier work of Ellis, we discuss a topological approach, first to the original theorem, and then to a generalization relaxing the ergodicity assumptions due to Austin.
The talk is based on joint work with Nikolai Edeko and Asgar Jamneshan.
This video is part of the Institute for Advanced Study‘s Special year research seminar.
