Application of high-low method to distance problems

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.

Name thesis:degree_name

Doctoral

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2023

Author dc:creator

• Zhang, Lingxian

Advisor dc:contributor.advisor

• Guth, Larry

Statement dc:rights

• In Copyright - Educational Use Permitted
• Copyright retained by author(s)

Licence dc:rights.uri

• https://rightsstatements.org/page/InC-EDU/1.0/

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/151380

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/151380