# Bryce McLaughlin

Harvey Mudd College Mathematics 2017

Thesis Proposal: | Applying the Polynomial Method to Problems in Discrete Geometry |
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Thesis Advisor: | Prof. Mohamed Omar |

Second Reader: | Prof. Dagan Karp |

E-Mail: | bmclaughlin@g.hmc.edu |

## Applying the Polynomial Method to Problems in Discrete Geometry

Since the mid-20th century, mathematicians have used the idea of
geometric incidences between sets of points and other objects
in ℝ^{k} to bound and solve problems in Discrete Geometry.
Recently, a result called the polynomial method has allowed us to strengthen
combinatorial incidence bounds iteratively, increasing the
effectiveness of using geometric incidences as a problem solving method.
In this thesis, we explore the inner workings of the polynomial method
and attempt to use it in attacking some open problems in Discrete Geometry.