2026-09-18T20:32:13Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1526352023-11-03T03:06:59Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Guth, Larry
Tammen, Sarah
Massachusetts Institute of Technology. Department of Mathematics
2023-11-02T20:04:36Z
2023-11-02T20:04:36Z
2023-09
2023-08-22T19:02:34.934Z
https://hdl.handle.net/1721.1/152635
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.
Ph.D.
Massachusetts Institute of Technology
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Incidence Problems for Slabs
Thesis
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Doctoral
Doctor of Philosophy
Publication
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