Date: Friday 4th October 2013 br Speaker: Daniel Plaumann br Title: Hyperbolic Polynomials and sums of squares br br Abstract: A real polynomial is hyperbolic if it denes a hypersurface consisting of maximally nested ovaloids. These polynomials appear in many areas of mathematics, including convex optimisation, combinatorics and differential equations. We investigate the relation between determinantal representations of hyperbolic polynomials and sums of squares representations of positive polynomials. In particular, we will explain the connection with matroid theory for the case of multi-affine polynomials coming from the work of Brndn, Wagner and Wei.