Title:
Additive stucture, rich lines, and exponential set-expansion
Additive stucture, rich lines, and exponential set-expansion
Authors
Borenstein, Evan
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Advisors
Croot, Ernest
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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.
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Date Issued
2009-05-19
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Dissertation