Representations and approximations of hyperbolicity cones

Algebra Seminar
Monday, August 20, 2012 - 3:00pm for 1 hour (actually 50 minutes)
Skiles 005
Daniel Plaumann – University of Konstanz
Greg Blekherman
Hyperbolic polynomials are real polynomials that can be thought of as generalized determinants. Each such polynomial determines a convex cone, the hyperbolicity cone. It is an open problem whether every hyperbolicity cone can be realized as a linear slice of the cone of psd matrices. We discuss the state of the art on this problem and describe an inner approximation for a hyperbolicity cone via a sums of squares relaxation that becomes exact if the hyperbolic polynomial possesses a symmetric determinantal representation. (Based on work in progress with Cynthia Vinzant)