CMSA Special Seminar: Differentials ideals for Calabi-Yau periods and Feynman integrals

We will review the connection between Feynman integrals and Calabi–Yau periods. Then we explain some properties of the period geometry, in particular the Picard–Fuchs differential ideal and to which extend it allows to calculate the Feynman integral. The main result is an explicit analytic calculation of the 3-Loop Banana graph with all mass parameters using relative periods on a special family of K3 surfaces.