6 citations · 15 across the 16 of their papers we have counts for
4 papers · 1 filter
Symmetric Hyperbolic Polynomials
Grigoriy Blekherman, Julia Lindberg, Kevin Shu
Hyperbolic polynomials have been of recent interest due to applications in a wide variety of fields. We seek to better understand these polynomials in the case when they are symmet…
Linear Principal Minor Polynomials: Hyperbolic Determinantal Inequalities and Spectral Containment
Grigoriy Blekherman, Mario Kummer, Raman Sanyal +2
A linear principal minor polynomial or lpm polynomial is a linear combination of principal minors of a symmetric matrix. By restricting to the diagonal, lpm polynomials are in bije…
Extreme Nonnegative Quadratics over Stanley Reisner Varieties
Kevin Shu
We consider the convex geometry of the cone of nonnegative quadratics over Stanley-Reisner varieties. Stanley-Reisner varieties (which are unions of coordinate planes) are amongst…
Sums of Squares and Sparse Semidefinite Programming
Grigoriy Blekherman, Kevin Shu
We consider two seemingly unrelated questions: the relationship between nonnegative polynomials and sums of squares on real varieties, and sparse semidefinite programming. This con…