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Characteristic Factors for Multiple Recurrence and Combinatorial Applications
Robertson, Donald

2015, Doctor of Philosophy, Ohio State University, Mathematics.
Since Furstenberg’s proof of Szemerédi’s theorem in the 1970s a mutually beneficial relationship has blossomed between ergodic theory and density Ramsey theory. In this thesis we contribute to this relationship by using the method of characteristic factors to prove some extensions and generalizations of Szemerédi’s theorem, building on recent work by many authors. Specifically, in Chapter 3 we prove a two-sided version of the Furstenberg correspondence theorem for amenable groups, in Chapter 4 we describe characteristic factors for correlations that generalize Szemerédi’s theorem to amenable groups, in Chapter 5 we enlarge the collections of polynomials for which the multidimensional polynomial Szemerédi theorem ins known to hold, and in Chapter 7 we prove that every large subset of an amenable group contains a two-sided finite products set.
Donald Bergelson (Advisor)
119 p.

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Robertson, D. (2015). Characteristic Factors for Multiple Recurrence and Combinatorial Applications. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Robertson, Donald. "Characteristic Factors for Multiple Recurrence and Combinatorial Applications." Electronic Thesis or Dissertation. Ohio State University, 2015. OhioLINK Electronic Theses and Dissertations Center. 23 Nov 2017.

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Robertson, Donald "Characteristic Factors for Multiple Recurrence and Combinatorial Applications." Electronic Thesis or Dissertation. Ohio State University, 2015. https://etd.ohiolink.edu/

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