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Monthly Archives: December 2013
Arithmetic progressions and the affine semigroup
— 1. Introduction — Van der Waerden’s theorem on arithmetic progressions states that, given any finite partition of , one of the cells contains arbitrarily long arithmetic progressions. For the sake of completion we give a precise formulation. Theorem 1 … Continue reading
Posted in Combinatorics, Topological Dynamics
Tagged proximal system, Szemeredi's theorem, van der waerden
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Convergence and Recurrence of Z actions
Ergodic Ramsey Theory started with Furstenberg’s proof of Szemeredi’s theorem in arithmetic progressions in 1977. Through a correspondence principle, Furstenberg realized that Szemeredi’s theorem follows from a dynamical statement: for every invertible, ergodic measure preserving transformation of a probability space … Continue reading
Posted in Ergodic Theory, State of the art
Tagged Austin, Bergelson, convergence, Conze, ergodic theorem, Furstenberg, Host, Katznelson, Kra, Leibman, Lesigne, Poincare, recurrence, Tao, Walsh
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