MIT Libraries logoDSpace@MIT

MIT
View Item 
  • DSpace@MIT Home
  • MIT Libraries
  • MIT Theses
  • Doctoral Theses
  • View Item
  • DSpace@MIT Home
  • MIT Libraries
  • MIT Theses
  • Doctoral Theses
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Application of high-low method to distance problems

Author(s)
Zhang, Lingxian
Thumbnail
DownloadThesis PDF (719.2Kb)
Advisor
Guth, Larry
Terms of use
In Copyright - Educational Use Permitted Copyright retained by author(s) https://rightsstatements.org/page/InC-EDU/1.0/
Metadata
Show full item record
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.
Date issued
2023-06
URI
https://hdl.handle.net/1721.1/151380
Department
Massachusetts Institute of Technology. Department of Mathematics
Publisher
Massachusetts Institute of Technology

Collections
  • Doctoral Theses

Browse

All of DSpaceCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

My Account

Login

Statistics

OA StatisticsStatistics by CountryStatistics by Department
MIT Libraries
PrivacyPermissionsAccessibilityContact us
MIT
Content created by the MIT Libraries, CC BY-NC unless otherwise noted. Notify us about copyright concerns.