Petter Brändén: The ubiquity of hyperbolic polynomials

Hyperbolic and stable polynomials are multivariate polynomials that generalize determinants and univariate polynomials with only real zeros. These polynomials originate in PDE theory and control theory. However, methods involving such polynomials have recently been used to settle open problems in combinatorics, C*-algebras, real algebraic geometry, optimization, probability theory and computer science. The most famous application being the solution to the Kadison–Singer problem by Marcus et. al. We give a broad overview of hyperbolic and stable polynomials and discuss some of the applications.

(inaugural lecture for newly appointed professor)