Jose Acevedo

activity

20152026

collaborators

5 papers

math.RA2026

Eigenvalues of locally positive semidefinite matrices: Non-convexity and Geometry

Jose Acevedo, Grigoriy Blekherman, Sebastian Debus +2

A real symmetric matrix is called $d$ -locally positive semidefinite if all of its $d \times d$ principal submatrices are positive semidefinite. We investigate the spectral geometry…

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 $n$ -variate real symmetric homogeneous polynomials (forms) of degree $d$ 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…

math.CO2015

Test Sets for Nonnegativity of Polynomials Invariant under a Finite Reflection Group

Jose Acevedo, Mauricio Velasco

A set $S \subset R^{n}$ is a nonnegativity witness for a set $U$ of real homogeneous polynomials if $F$ in $U$ is nonnegative on $R^{n}$ if and only if it is nonnegati…