80 citations · 232 across the 22 of their papers we have counts for
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math.AG2012★ 29 cited
Hyperbolic polynomials, interlacers, and sums of squares
Mario Kummer, Daniel Plaumann, Cynthia Vinzant
Hyperbolic polynomials are real polynomials whose real hypersurfaces are nested ovaloids, the inner most of which is convex. These polynomials appear in many areas of mathematics,…
math.AG2012
Determinantal representations of hyperbolic curves via polynomial homotopy continuation
Anton Leykin, Daniel Plaumann
A smooth curve in the real projective plane is hyperbolic if its ovals are maximally nested. By the Helton-Vinnikov Theorem, any such curve admits a definite symmetric determinanta…
math.AG2012★ 62 cited
Determinantal representations of hyperbolic plane curves: An elementary approach
Daniel Plaumann, Cynthia Vinzant
If a real symmetric matrix of linear forms is positive definite at some point, then its determinant is a hyperbolic hypersurface. In 2007, Helton and Vinnikov proved a converse in…