Turán problems in extremal combinatorics ask to find asymptotic bounds on the edge
densities of graphs and hypergraphs that avoid specified subgraphs. The theory of flag …

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

This chapter investigates how symmetries can be used to reduce the computational
complexity in polynomial optimization problems. A focus will be specifically given on the …

For given integers n and d, both at least 2, we consider a homogeneous multivariate
polynomial f_d of degree d in variables indexed by the edges of the complete graph on n …

Every convex homogeneous polynomial (or form) is nonnegative. Blekherman has shown
that there exist convex forms that are not sums of squares via a nonconstructive argument …

Establishing inequalities among graph densities is a central pursuit in extremal
combinatorics. A standard tool to certify the nonnegativity of a graph density expression is to …