Convex sets arising in a variety of applications are well-defined for every relevant
dimension. Examples include the simplex and the spectraplex that correspond, respectively …

A real univariate polynomial of degree n is called hyperbolic if all of its n roots are on the real
line. Such polynomials appear quite naturally in different applications, for example, in …

We study symmetric non-negative forms and their relationship with symmetric sums of
squares. For a fixed number of variables n and degree 2 d, symmetric non-negative forms …

This paper studies Positivstellens\" atze and moment problems for sets that are given by
universal quantifiers. Let $ Q $ be a closed set and let $ g=(g_1,..., g_s) $ be a tuple of …

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 …

Let K be a field and (f 1,…, fs, ϕ) be multivariate polynomials in K [x 1,…, xn](with s< n) each
invariant under the action of S n, the group of permutations of {1,…, n}. We consider the …

Let R be a real closed field. We consider basic semi-algebraic sets defined by n-variate
equations/inequalities of s symmetric polynomials and an equivariant family of polynomials …

In this paper, we consider the problem of deciding the existence of real solutions to a system
of polynomial equations having real coefficients, and which are invariant under the action of …

This paper describes the structure of invariant skew fields for linear actions of finite solvable
groups on free skew fields in d generators. These invariant skew fields are always finitely …

We study symmetric nonnegative forms and their relationship with symmetric sums of
squares. For a fixed number of variables $ n $ and degree $2 d $, symmetric nonnegative …