10 papers · 1 filter
Nonnegative Polynomials and Moment Problems on Algebraic Curves
Lorenzo Baldi, Grigoriy Blekherman, Rainer Sinn
The cone of nonnegative polynomials is of fundamental importance in real algebraic geometry, but its facial structure is understood in very few cases. We initiate a systematic stud…
Stubborn Polynomials
Lorenzo Baldi, Grigoriy Blekherman, Khazhgali Kozhasov +3
The relationship between nonnegative polynomials and sums of squares is a classical topic in real algebraic geometry. We study \emph{stubborn polynomials} on a real variety …
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…
The Wonderful Geometry of the Vandermonde map
Jose Acevedo, Grigoriy Blekherman, Sebastian Debus +1
We study the geometry of the image of the nonnegative orthant under the power-sum map and the elementary symmetric polynomials map. After analyzing the image in finitely many varia…
Pythagoras Numbers for Ternary Forms
Grigoriy Blekherman, Alex Dunbar, Rainer Sinn
We study the Pythagoras numbers of real ternary forms, defined for each degree as the minimal number such that every degree ternary form which is a sum of…
Nonnegativity certificates on real algebraic surfaces
Grigoriy Blekherman, Rainer Sinn, Gregory G. Smith +1
We introduce tools for transferring nonnegativity certificates for global sections between line bundles on real algebraic surfaces. As applications, we improve Hilbert's degree bou…