Bryce McLaughlin

Harvey Mudd College Mathematics 2017

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Thesis Proposal: Applying the Polynomial Method to Problems in Discrete Geometry
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 ℝk 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.