Speaker: Sean O’Rourke, University of Colorado Boulder
Title: Critical Points of Random Polynomials
Abstract: Consider a polynomial p in one complex variable. The Gauss-Lucas theorem states that the critical points of p lie inside the convex hull of the zeros. But how are the critical points distributed inside the convex hull if p is chosen randomly? In this talk, I will discuss several models of random polynomials and their critical points. For a natural model, where the roots are chosen independently, I will explain how each root typically comes paired with one critical point and discuss the typical distance between each root and its paired critical point. This talk is based on joint work with Noah Williams.
Host: Dr. Mark Meckes, Associate Professor, Case Western Reserve University