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    Additive stucture, rich lines, and exponential set-expansion

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    borenstein_evan_s_200908_phd.pdf (313.7Kb)
    Date
    2009-05-19
    Author
    Borenstein, Evan
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    Abstract
    We will survey some of the major directions of research in arithmetic combinatorics and their connections to other fields. We will then discuss three new results. The first result will generalize a structural theorem from Balog and Szemerédi. The second result will establish a new tool in incidence geometry, which should prove useful in attacking combinatorial estimates. The third result evolved from the famous sum-product problem, by providing a partial categorization of bivariate polynomial set functions which induce exponential expansion on all finite sets of real numbers.
    URI
    http://hdl.handle.net/1853/29664
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    • Georgia Tech Theses and Dissertations [22398]
    • School of Mathematics Theses and Dissertations [399]

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