Polynomial partitioning and incidence problems in higher dimensions
Author(s)Yang, Ben, Ph. D. Massachusetts Institute of Technology
Massachusetts Institute of Technology. Department of Mathematics.
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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..
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2017.Cataloged from PDF version of thesis.Includes bibliographical references (pages 57-59).
DepartmentMassachusetts Institute of Technology. Department of Mathematics.; Massachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology