Ramsey Theory, Uniform Distribution, and Ergodic Theory
Vitaly Bergelson
Abstract.
The goal of this mini-series is to give a glimpse of the
multifaceted connections of ergodic theory with and applications to
combinatorics, number theory and the theory of uniform
distribution.
Tentative list of topics:
- Partition Ramsey theory and topological dynamics
- Szemeredi's theorem and Furstenberg's correspondence theorem
- Van der Corput's trick and polynomial extensions of the Szemeredi theorem
- Topological algebra in
and Hindman's theorem
- Bohr compactifications and properties of large sets
- Rotations on nilmanifolds and the uniform distribution of generalized
polynomials
- Ergodic Ramsey theory and amenable groups
- Green-Tao theorem on progressions in primes
- Open problems and conjectures