joint work with Daniel Plaumann, Stephan Weis
Kippenhahn’s Theorem relates the numerical range of a complex square matrix to a hyperbolic plane curve via convex duality. We will discuss this result and its generalization to higher dimensions (which goes by the name of joint numerical ranges of a sequence of hermitian matrices) from the point of view of convex algebraic geometry.
We present a new small spectrahedral relaxation of hyperbolicity cones that relies on the Helton-Vinnikov theorem and exhibit certain cases where it is exact.