Sarah Hess

collaborators

3 papers

math.AG2024

Separating Cones defined by Toric Varieties: Some Properties and Open Problems

Charu Goel, Sarah Hess, Salma Kuhlmann

In 1888, Hilbert proved that the cone $P_{n + 1, 2 d}$ of positive semidefinite forms in $n + 1$ variables of degree $2 d$ coincides with its subcone $Σ_{n + 1, 2 d}$ of those forms…

math.AG2024

A Refinement of Hilbert's 1888 Theorem: Separating Cones along the Veronese Variety

Charu Goel, Sarah Hess, Salma Kuhlmann

For $n, d \in N$ , the cone $P_{n + 1, 2 d}$ of positive semi-definite (PSD) $(n + 1)$ -ary $2 d$ -ic forms (i.e., homogeneous polynomials with real coefficients in $n + 1$ var…

math.AG2023

Intermediate Cones between the Cones of Positive Semidefinite Forms and Sums of Squares

Charu Goel, Sarah Hess, Salma Kuhlmann

The cone $P_{n + 1, 2 d}$ ( $n, d \in N$ ) of all positive semidefinite (PSD) real forms in $n + 1$ variables of degree $2 d$ contains the subcone $Σ_{n + 1, 2 d}$ of those that…