Speaker
Description
Feynman integrals associated with geometries beyond the Riemann sphere, such as elliptic curves, K3 surfaces, and Calabi-Yau manifolds, are playing an increasingly important role in modern precision calculations, from collider physics to gravitational-wave theory. A systematic way to evaluate these integrals is through differential equations, with the goal of casting them into
epsilon-form, where their analytic behaviour and transcendental structure become more transparent.
In this talk, I will discuss the connection between leading singularities and canonical bases for Feynman integrals beyond the realm of multiple polylogarithms. In particular, I will show how the transcendental functions needed to describe the differential equation matrix of a canonical system can be identified directly from the integrand. The discussion will be illustrated through examples of increasing complexity involving the interplay of several geometries, including elliptic curves, K3 surfaces, and Calabi-Yau threefolds.
