Speaker
Description
Precision predictions for collider and gravitational-wave observables rely on the efficient evaluation and reduction of multi-loop Feynman integrals. I will present a method for constructing differential equations for Feynman integrals directly from multivariate intersection numbers, bypassing the solution of large systems of integration-by-parts identities. The method exploits the large-$\varepsilon$ expansion of intersection numbers, whose coefficients are known as higher residue pairings. These pairings are naturally defined for analytically regulated integrals; in the vanishing-regulator limit, they recover the relative cohomology framework, leading to a drastic simplification of the resulting formulae. The pairings localise at the critical points of the associated potential, organising the computation sector by sector, while the corresponding sums over critical points can be evaluated purely algebraically using companion-matrix techniques. As an application, I will construct canonical differential equations for massless planar ladder integrals up to four loops.