Undecidability of polynomial inequalities in weighted graph homomorphism densities - Grigoriy Blekherman; Annie Raymond; Fan Wei (Forum of Mathematics, Sigma, 2024)
Many problems and conjectures in extremal combinatorics concern polynomial inequalities between homomorphism densities of graphs where we allow edges to have real weights. Using the theory of graph limits, we can equivalently evaluate polynomial expressions in homomorphism densities on kernels W, that is, symmetric, bounded and measurable functions W from