MATH 254A : Topics in Ergodic Theory
Course description: Basic ergodic
theorems (pointwise, mean, maximal) and recurrence theorems (Poincare,
Khintchine, etc.) Topological
dynamics. Structural theory of
measure-preserving systems; characteristic factors. Spectral theory of dynamical
systems. Multiple recurrence
theorems (Furstenberg, etc.) and connections with additive combinatorics
(e.g. Szemerédi’s theorem).
Orbits in homogeneous spaces, especially nilmanifolds;
Ratner’s theorem. Further
topics as time allows may include joinings, dynamical entropy, return
times theorems, arithmetic progressions in primes, and/or
