Polynomial partitioning and incidence problems in higher dimensions
Name
1014342767-MIT.pdf
Description
Full printable version
Size
2.77 MB
Format
Adobe PDF
Checksum (MD5)
ad9c24d275ee0436a3946a45c571e97d
Author(s)
Yang, Ben, Ph. D. Massachusetts Institute of Technology
Advisor(s)
Lawrence Guth.
Date Issued
2017
Publisher
Massachusetts Institute of Technology
Abstract
Incidence geometry is the study of the intersection patterns of simple geometric objects. One of the breakthroughs in this field is the polynomial partitioning technique introduced by Guth and Katz. In this thesis, I will present two results on incidence problems with high-dimensional objects: an almost tight bound on the number of joints formed by varieties in Rn and a tight bound on the number of flags in Rn. The proofs are based on the polynomial partitioning technique and its variations..
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2017.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 57-59).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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