## Real rooted polynomials and multivariate extensions

Adam Marcus

Princeton University; von Neumann Fellow, School of Mathematics

October 18, 2016

I will introduce two notions that generalize the idea of real rootedness to multivariate polynomials: real stability and hyperbolicity. I will then show two applications of these types of polynomials that will (hopefully) be of interest to the CS audience---Gurvits' method for lower bounding the permanent and a generalization of semidefinite programming known as hyperbolic programming.