Mr. Boris Hanin, Northwestern University
Colloquium Title: Correlations and Pairing of Zeros and Critical Points of Random Polynomials
Abstract: The Gauss-Lucas theorem states that the critical points of a polynomial in one complex variable lie inside the convex hull of its zeros. Motivated by this, I will present some results about the geometry of zeros and critical points of random polynomials. I will explain that, in fact, zeros and critical points appear in rigid pairs, I will try to give some intuition from physics for why this pairing should appear in the first place.