Vitaly Bergelson studies the interaction of ergodic theory with Ramsey theory and arithmetic patterns. His Ohio State publication list documents work on recurrence, polynomial configurations and semigroup actions.[ref]
https://people.math.osu.edu/bergelson.1/. Author publication list
His Ergodic Ramsey Theory - an update by Vitaly Bergelson develops the exchange between recurrence in dynamical systems and structured configurations in subsets of integers. With Neil Hindman and Kendall Williams, he also extended Milliken–Taylor theorem patterns to polynomial settings, using algebraic properties of ultrafilters to obtain monochromatic configurations.[ref]
Ergodic Ramsey Theory - an update by Vitaly Bergelson. Survey overview
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