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thesis.pdf (750.38 KB)
ETD Abstract Container
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Characteristic Factors for Multiple Recurrence and Combinatorial Applications
Author Info
Robertson, Donald
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1429633268
Abstract Details
Year and Degree
2015, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
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.
Committee
Vitaly Bergelson (Advisor)
Pages
119 p.
Subject Headings
Mathematics
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Citations
Robertson, D. (2015).
Characteristic Factors for Multiple Recurrence and Combinatorial Applications
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1429633268
APA Style (7th edition)
Robertson, Donald.
Characteristic Factors for Multiple Recurrence and Combinatorial Applications.
2015. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1429633268.
MLA Style (8th edition)
Robertson, Donald. "Characteristic Factors for Multiple Recurrence and Combinatorial Applications." Doctoral dissertation, Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1429633268
Chicago Manual of Style (17th edition)
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Document number:
osu1429633268
Download Count:
917
Copyright Info
© 2015, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.