| dc.contributor.advisor | Guth, Larry | |
| dc.contributor.author | Tammen, Sarah | |
| dc.date.accessioned | 2023-11-02T20:04:36Z | |
| dc.date.available | 2023-11-02T20:04:36Z | |
| dc.date.issued | 2023-09 | |
| dc.date.submitted | 2023-08-22T19:02:34.934Z | |
| dc.identifier.uri | https://hdl.handle.net/1721.1/152635 | |
| dc.description.abstract | 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. | |
| dc.publisher | Massachusetts Institute of Technology | |
| dc.rights | Attribution-ShareAlike 4.0 International (CC BY-SA 4.0) | |
| dc.rights | Copyright retained by author(s) | |
| dc.rights.uri | https://creativecommons.org/licenses/by-sa/4.0/ | |
| dc.title | Incidence Problems for Slabs | |
| dc.type | Thesis | |
| dc.description.degree | Ph.D. | |
| dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | |
| mit.thesis.degree | Doctoral | |
| thesis.degree.name | Doctor of Philosophy | |
