Tutte seminar - David Wagner

Multivariate stable polynomials

Abstract:

Univariate polynomials with only real roots -- while special -- do occur often enough that their properties lead to interesting conclusions in diverse areas. Due mainly to the recent work of two young mathematicians, Julius Borcea and Petter Brändén, a very successful multivariate generalization of this method has been developed. In this talk I'll survey some of the main results of this theory, including the Grace-Walsh-Szegő Theorem and Borcea and Brändén's generalization of the Pólya-Schur Theorem.