Incidence Problems for Slabs

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.

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

• Tammen, Sarah

Advisor dc:contributor.advisor

• Guth, Larry

Statement dc:rights

• Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)
• Copyright retained by author(s)

Licence dc:rights.uri

• https://creativecommons.org/licenses/by-sa/4.0/

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/152635

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/152635