Application of high-low method to distance problems
Author(s)
Zhang, Lingxian
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Advisor
Guth, Larry
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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.
Date issued
2023-06Department
Massachusetts Institute of Technology. Department of MathematicsPublisher
Massachusetts Institute of Technology