Kaylee Weatherspoon, Rutgers University

Abstract

Given a collection of n points and m lines in the plane, we say a point x is incident to a line L if the point x lies on the line L. We will state and prove one of my favorite theorems, which bounds the number of incidences in an arbitrary collection of points and lines subject to certain minimal constraints.

We will see the importance of this result to an open graph drawing problem, a discrete geometry problem, and one of the most famous conjectures of Erdős himself.

See: https://sites.math.rutgers.edu/~kmg326/GCS/GCS.html