Intersection numbers from higher-order partial differential equations

We propose a new method for the evaluation of intersection numbers for twisted meromorphic n-forms, through Stokes’ theorem in n dimensions. It is based on the solution of an n-th order partial differential equation and on the evaluation of multivariate residues. We also present an algebraic expression for the contribution from each multivariate residue. We illustrate our approach with a number of simple examples from mathematics and physics.