Mario Kummer (TU Berlin): Rational representations of plane spectrahedra

Abstract: A central open question in convex algebraic geometry is whether every hyperbolicity region is a spectrahedron, i.e. defined by a linear matrix inequality. It follows from a theorem by Helton and Vinnikov that this is true in the plane. However the entries of the matrices resulting from their construction are typically algebraic numbers of large degree. We construct a representation with rational matrices provided that the hyperbolic polynomial is defined over the rational numbers. This is joint work with Simone Naldi and Daniel Plaumann.