Vector Spaces of Generalized Euler Integrals

We study vector spaces associated to a family of generalized Euler integrals. Their dimension is given by the Euler characteristic of a very affine variety. Motivated by Feynman integrals from particle physics, this has been investigated using tools from homological algebra and the theory of D-modules. We present an overview and discuss relations between these approaches. This is an ongoing project with Daniele Agostini, Anna-Laura Sattelberger, and Simon Telen.