Ergodic Ramsey theory

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Shortly after Szemerédi's proof that a set of positive upper density contains arbitrarily long arithmetic progressions, Hillel Furstenberg gave a new proof of this theorem using ergodic theory. This gave rise to the field of ergodic Ramsey theory, in which problems motivated by additive combinatorics are proven using ergodic theory. Ergodic Ramsey theory has since produced combinatorial results, some of which have yet to be obtained by other means, and has also given a deeper understanding of the structure of Measure-preserving dynamical systems.

[edit] See also

• Ramsey theory
• Syndetic set
• Piecewise syndetic set
• Thick set
• IP set

[edit] References

• Ergodic Methods in Additive Combinatorics
• Ergodic Ramsey Theory -an Update
• Randall McCutcheon (1999). Elemental Methods in Ergodic Ramsey Theory. Springer. ISBN 978-3540668091.