This textbook originates from a course for graduate students that I taught at Konstanz
University approximately five or six times over the past twenty years. While the first part of the …

We consider cones of real forms which are sums of squares and invariant under a (finite)
reflection group. Using the representation theory of these groups we are able to use the …

This document describes our freely distributed Maple library spectra, for Semidefinite
Programming solved Exactly with Computational Tools of Real Algebra. It solves linear …

The minimum number of observations such that the maximum likelihood estimator in a
Gaussian graphical model exists with probability one is called the maximum likelihood …

This paper explores the geometric structure of the spectrahedral cone, called the symmetry
adapted positive semidefinite (PSD) cone, and the symmetry adapted Gram spectrahedron …

A celebrated result by Hilbert says that every real nonnegative ternary quartic is a sum of
three squares. We show more generally that every nonnegative quadratic form on a real …

We consider the problem of minimizing a linear function over an affine section of the cone of
positive semidefinite matrices, with the additional constraint that the feasible matrix has …

We consider the geometry associated to the ambiguities of the one-dimensional Fourier
phase retrieval problem for vectors in C^N+1. Our first result states that the space of signals …

DOI: https://doi. org/10.1090/noti2280 function 2 (𝑥2− 𝑦𝑧)+ 1 is a sum of squares modulo
the defining equation of the unit sphere, so this function is nonnegative on the sphere. Thus …

Abstract The Gram spectrahedron Gram (f) of a form f with real coefficients is a compact
affine-linear section of the cone of psd symmetric matrices. It parametrizes the sum of …