Coproducts of Multi-Loop Feynman Integrals

It is known that for one loop Feynman integrals there is a correspondence between a certain graphical coproduct and the coproduct of polylogarithms. It has recently been conjectured that the coproduct of a general integral may be expressed in a simple form (the so called master formula) involving master integrals and their corresponding contours. We seek to apply this idea to multi-loop Feynman integrals evaluating to Hypergeometric type functions to derive examples of a graphical coproduct beyond one loop. We will also explore the possible coproduct structure on elliptic functions required for the study of more general multi-loop integrals. Eventually it is hoped to obtain a fully general graphical coproduct for multi-loop integrals.