5 papers
A semidefinite programming characterization of the Crawford number
Shmuel Friedland, Cynthia Vinzant
We give a semidefinite programming characterization of the Crawford number. We show that the computation of the Crawford number within precision is computable in poly…
Moments, Sums of Squares, and Tropicalization
Grigoriy Blekherman, Felipe Rincón, Rainer Sinn +2
We use tropicalization to study the duals to cones of nonnegative polynomials and sums of squares on a semialgebraic set . The truncated cones of moments of measures supported o…
Tropicalizing Principal Minors of Positive Definite Matrices
Abeer Al Ahmadieh, Felipe Rincón, Cynthia Vinzant +1
We study the tropicalization of the image of the cone of positive definite matrices under the principal minors map. It is a polyhedral subset of the set of -concave functions on…
The convex algebraic geometry of higher-rank numerical ranges
Jonathan Nino-Cortes, Cynthia Vinzant
The higher-rank numerical range is a convex compact set generalizing the classical numerical range of a square complex matrix, first appearing in the study of quantum error correct…
Every real-rooted exponential polynomial is the restriction of a Lee-Yang polynomial
Lior Alon, Alex Cohen, Cynthia Vinzant
A Lee-Yang polynomial is a polynomial that has no zeros in the polydisc and its inverse $ (\mathbb{C}\setminus\overline{\mathbb{D}})^{n…