92 citations · 253 across the 22 of their papers we have counts for
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Sums of Squares: A Real Projective Story
Grigoriy Blekherman, Rainer Sinn, Gregory G. Smith +1
The relationship between nonnegative polynomials and sums of squares is one of the central questions in real algebraic geometry. A modern approach is to look at nonnegative polynom…
Sums of Squares and Quadratic Persistence on Real Projective Varieties
Grigoriy Blekherman, Rainer Sinn, Gregory G. Smith +1
We bound the Pythagoras number of a real projective subvariety: the smallest positive integer such that every sum of squares of linear forms in its homogeneous coordinate ring…
Do Sums of Squares Dream of Free Resolutions?
Grigoriy Blekherman, Rainer Sinn, Mauricio Velasco
We associate to a real projective variety two convex cones which are fundamental in real algebraic geometry: the cone of quadratic forms nonnegative on , and the cone…
Sharp Degree Bounds for Sum-of-Squares Certificates on Projective Curves
Grigoriy Blekherman, Gregory G. Smith, Mauricio Velasco
Given a real projective curve with homogeneous coordinate ring R and a nonnegative homogeneous element f in R, we bound the degree of a nonzero homogeneous sum-of-squares g in R su…
Gap vectors of real projective varieties
Grigoriy Blekherman, Sadik Iliman, Martina Juhnke-Kubitzke +1
Let be a totally real, non-degenerate, projective variety and let be a generic set of points. Let be the cone of nonnegativ…
Dual toric codes and polytopes of degree one
Valérie Gauthier Umaña, Mauricio Velasco
We define a statistical measure of the typical size of short words in a linear code over a finite field. We prove that the dual toric codes coming from polytopes of degree one are…