Mathematical Conversations

Hyperbolic polynomials are a multivariate generalization of real-rooted polynomials that originated in the study of partial differential equations and have since found applications in many other fields, including operator theory, optimization, and combinatorics. One motivating example comes from the determinant of a symmetric matrix, and many fundamental properties of eigenvalues can be derived from this more general context. In this talk, I will survey some of the beautiful geometry underlying these polynomials and a sampling of their applications.