Speaker
Description
I will discuss how intersection theory controls the algebra of Feynman integrals, and show how their direct decomposition onto a basis of master integrals can by achieved by projection, using intersection numbers. After introducing a few basics concepts of intersection theory, I will show the application of this novel method, first, to special mathematical functions, and, later, to Feynman integrals on the maximal cuts, also explaining how differential equations and dimensional recurrence relations for master integrals can be directly built by means of intersection numbers. The presented method exposes the geometric structure beneath Feynman integrals, and offers the computational advantage of bypassing the system-solving strategy characterizing the reduction algorithms based on integration-by-parts identities.
