Ponente
Descripción
Feynman integrals are the universal building blocks of perturbative Quantum Field Theory (QFT) and are hence of great interest both for a better understanding of the general structure of QFT as well as for practical calculations. However they are notoriously difficult to evaluate, in particular if many particles and scales are involved. Over the last decade or so, it has been realized that one can associate a certain geometry to a given Feynman integral, allowing us to leverage geometric information to solve the integral. Integrals associated with the simplest geometry, the Riemann sphere, are well under control and also in the study of integrals associated to elliptic curves (the simplest non-trivial geometry appearing) we have seen tremendous progress. Beyond these cases however, our understanding is still very limited. In this talk I will review the differential equations method, the most powerful method of solving Feynman integrals, with a particular emphasis on the use of geometric information. I will then explain how this method can be generalized to Feynman integrals involving hyperelliptic curves, certain higher-genus generalizations of elliptic curves.“
