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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

        Instructor: Terence Tao, tao@math.ucla.edu, x64844, MS 6183