MATH 663-601
Ergodic Theory
Fall 2019
Instructor: David Kerr
Office: Blocker 525K
Office hours: W 10:00-11:30, or by appointment
Lectures: TR 12:45-2:00, BLOC 205B
Course description: The course will be an introduction to the theory of measure-preserving group actions on probability spaces and will also include some topological dynamics. The main topics will be ergodicity, weak mixing, compactness, dynamical tilings, entropy, and orbit equivalence. Emphasis will be given to the relationship between these dynamical phenomena and structural properties of groups such as amenability, property (T), and soficity. No background in ergodic theory is required, but some basic functional analysis will be assumed (e.g., operators on Hilbert space).
Resources:
  • David Kerr and Hanfeng Li. Ergodic Theory: Independence and Dichotomies. Springer, Cham, 2016.
The following books are also recommended:
  • Karl Petersen. Ergodic Theory. Cambridge University Press, Cambridge, 1989.
  • Peter Walters. An Introduction to Ergodic Theory. Springer, New York, 2000.
Assignment: submit solutions to at least five problems from a list to be posted (due December 10).