Max Aires, Rutgers University

Abstract

A recurring problem in extremal discrete geometry is to ask for an upper or lower bound on the number of instances of a certain configuration in a set of n points. Important examples of this include the number of lines through k or more points (answered in the famous Szemeredi-Trotter Theorem), and the number of pairs of points at a fixed distance. In this talk, we consider the number of angles with a given measure alpha from n points in the plane, and derive an upper bound of O(n^2 log(n)) from Pach and Sharir. We then show that this bound can be achieved for many values of alpha.

This seminar is being held in person in The Hill Center,
Mathematics Graduate Student Lounge - 7th Floor
and online via a simultaneous broadcast on Zoom.
Zoom Link: https://rutgers.zoom.us/j/97170484433

Password: 102958

For further information see: https://sites.math.rutgers.edu/~ctk47/GCS.html