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Incidence Problems for Slabs

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Tammen-setammen-phd-math-2023-thesis.pdf

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Author(s)
Tammen, Sarah
Advisor(s)
Guth, Larry
Date Issued
September 2023
Publisher
Massachusetts Institute of Technology
Abstract
In this thesis, I prove incidence estimates for slabs which are formed by intersecting small neighborhoods of well-spaced hyperplanes in R superscript 𝑑 with the unit cube [0, 1] superscript 𝑑 . My work is an analogue of a theorem of Guth, Solomon, and Wang, who proved a version of the SzemerédiTrotter theorem for thin tubes that satisfy a certain strong spacing condition. My proof uses induction on scales and the high-low method of Vinh, along with new geometric insights.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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