MATH 663
Ergodic Theory
Fall 2014
Instructor: David Kerr
Office: Blocker 525L
Office hours: M 2:00-3:00, T 2:00-3:30
Lectures: MWF 11:30-12:20, BLOC 202
Course description: The course will be an introduction to the theory of measure-preserving group actions on probability spaces. The main topics will be ergodicity, weak mixing, compactness, and entropy. 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: Course notes. The following books are also recommended:
  • Eli Glasner. Ergodic Theory via Joinings. American Mathematical Society, Providence, RI, 2003.
  • Karl Petersen. Ergodic Theory. Cambridge University Press, Cambridge, 1989.
  • Peter Walters. An Introduction to Ergodic Theory. Springer-Verlag, New York, 2000.
Assignment: submit solutions to at least five of these problems (due December 17).