Ergodic Ramsey theory
Ergodic Ramsey theory is a branch of mathematics where problems motivated by additive combinatorics are proven using ergodic theory. == History == Ergodic Ramsey theory arose shortly after Endre Szemerédi's proof that a set of positive upper density contains arbitrarily long arithmetic progressions, when Hillel Furstenberg gave a new proof of this theorem using ergodic theory.