Date of Award

Spring 4-2016

Embargo Period

3-21-2017

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematical Sciences

Advisor(s)

Boris Bukh

Abstract

We study several problems in discrete geometry and extremal combinatorics. Discrete geometry studies the combinatorial properties of finite sets of simple geometric objects. One theme of the field is geometric Ramsey theory. Given m geometric objects, we want to select a not too small subset forming a configuration that is “regular” in some sense.

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