Roots of the Kac polynomials
Abstract: The Kac polynomial is one of the most studied models of random polynomials. It has numerous connections with other areas such as ODEs, number theory, and cryptography. We will touch on these connections and survey recent results and conjectures concerning a number of aspects of the root distribution: large-n limits, hole radii, real roots, and flow of roots under repeated derivatives.
Bio: Oanh Nguyen is an assistant professor in the Division of Applied Mathematics at Brown University. She graduated from Yale University in 2017. Before moving to Brown, Oanh held positions at Princeton University and the University of Illinois. She works on probability theory, stochastic processes and their applications. She received an NSF grant, AIM SQuaREs, and a Salomon research award from Brown University.