Partial fraction decompositions on hyperplane arrangements

Partial fraction decompositions (PFDs) of rational functions in several variables appear frequently in physics. Examples include abstract applications, such as the re-casting of scattering amplitudes as canonical forms of polytopes, and computational applications like developing efficient algorithms to compute Feynman integrals. Despite their ubiquity in physics, studies of PFDs seldom appear in mathematical literature. In this talk I will present an analysis of a specific class of PFDs, using the tools commutative algebra. I will then present an algorithm for computing these PFDs.