Application of high-low method to distance problems
Name
Zhang-Lingxian-phd-math-2023-thesis-pdf.pdf
Description
Thesis PDF
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719.24 KB
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Adobe PDF
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Author(s)
Zhang, Lingxian
Advisor(s)
Guth, Larry
Date Issued
June 2023
Publisher
Massachusetts Institute of Technology
Abstract
In this thesis, I used the high-low method to study incidence problems arising form variants of the distance set conjectures.
In the complex space, my collaborator Sarah Tammen and I proved analogues of the incidence estimates of Guth, Solomon and Wang \cite{WellSpacedTubes} for tubes obeying strong spacing conditions, and we used one of our new estimates to resolve a discretized variant of Falconer's distance set problem in C².
In the real space, I proved an incidence estimate for special boxes in R⁶, and used the estimate to derive a bound for a discretized variant of Falconer's problem in R³.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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