Polynomial partitioning and incidence problems in higher dimensions

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..

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2017

Author dc:creator

• Yang, Ben, Ph. D. Massachusetts Institute of Technology

Advisor dc:contributor.advisor

• Lawrence Guth.

• Mathematics.

Statement dc:rights

• MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/112880

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/112880