Graphical Differential Equations for Feynman Integrals

Recently it has been realized that large classes of Feynman integrals satisfy sets of differential equations that can be read off directly from the graph. This is interesting both from a conceptual point of view, since the origin of most of these differential equations is somewhat mysterious, as well as practically, as one could potentially use these differential equations to directly bootstrap the Feynman integrals. In this talk I will review these developments and discuss some open problems which could provide natural points of contact between physics and mathematics, in particular in the form of D-module theory.