PIMS-UVic Discrete Math Seminar: Kenneth Moore

A broad class of problems in extremal geometry can be characterized as follows. Fix a positive integer k and a property of k-tuples of points in R^2. The problem is then to determine how many k-tuples in an n-point set in R^2 can have the chosen property. One of the most famous instances of this form of problem is the unit distance problem, asked by Erdős in 1946. Here, the special property is pairs of points being precisely distance one apart. Another pair of well-studied open problems is to determine the maximum number of triples that determine a triangle of unit area or unit perimeter. In this presentation we will discuss recent progress on these triangle problems, particularly our new bounds on the number of unit perimeter triangles from earlier this year.

This talk is based on a joint work with Ritesh Goenka and Ethan White.