Eli Shamovich, Department of Pure Mathematics, University of Waterloo
"Real Fibered Morphism and Definite Determinantal Representations"
Stable and hyperbolic polynomials arose in the study of differential equations. These polynomials give rise to real projective hypersurfaces with interesting convexity properties. These convexity properties are used both in pure and applied mathematics (Kadison-Singer and optimization for example). A good way to certify hyperbolicity is to produce a definite determinant representation. Unfortunately, this is not always possible. In this talk I will present a generalization of the hyperbolic property to morphisms between real projective varieties. I will also discuss the notion of determinant representation and definite Ulrich sheaves and show how the two notions relate. Time permitting, I will describe an algorithm to construct definite Ulrich sheaves on hyperbolic curves using theta functions with certain special characteristics on the normalization.
This talk is based on joint works with V. Vinnikov and M. Kummer.