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Seminar Details

Crossings, Incidences, and Unit Triangles (A Story with a Happy Ending)

  • Start Date: March 20, 2024
  • Event Start Time: 12:15 PM
  • Event End Time: 1:15 PM
  • Seminar Series: Graduate Combinatorics Seminar
  • Presenter(s): Kaylee Weatherspoon - Rutgers University
  • Event Location: Mathematics Graduate Student Lounge -- 7th Floor | Rutgers University | Hill Center | Mathematics Department
  • Event Additional Info: <p>See:&nbsp;<a href="https://sites.math.rutgers.edu/~kmg326/GCS/GCS.html">https://sites.math.rutgers.edu/~kmg326/GCS/GCS.html</a></p>
  • Presentation Type: Stand Alone Presentation
  • 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.