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math.AG2024
Symmetric nonnegative functions, the tropical Vandermonde cell and superdominance of power sums
Jose Acevedo, Grigoriy Blekherman, Sebastian Debus +1
We study nonnegative and sums of squares symmetric (and even symmetric) functions of fixed degree. We can think of these as limit cones of symmetric nonnegative polynomials and sym…
math.AG2023
Power mean inequalities and sums of squares
Jose Acevedo, Grigoriy Blekherman
For fixed degree and increasing number of variables the dimension of the vector space of -variate real symmetric homogeneous polynomials (forms) of degree stabilizes. We stu…
math.AG2023
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…