Calabi-Yau geometry of the N-loop sunset Feynman integrals

In this talk we will discuss the algebraic and transcendental features of the computation of multiloop sunset Feynman integrals.
We will explain how the “creative telescoping” algorithm allows to derive efficiently the inhomogeneous differential equations satisfied by any Feynman integrals. 
In the case of the sunset integral we will show how the results can be understood by understanding the geometry and the moduli of the Calabi-Yau varieties of the sunset graph. In particular how the specialization of physical parameters leads to rank jump in the differential equation.
We will describe the appearance of a motivic elliptic curve in two loop graphs and how this allows to easily derive as differential equation system  efficiently.
This is based on work done in collaboration with Charles Doran and Andrey Novoseltsev