A hypergeometric view on banana integrals and beyond

by Dr Saiei Matsubara (Tohoku University)

Thursday 5 Mar 2026, 13:00 → 14:00 Europe/Berlin

A.1.01 - Alps Süd (MPP)

In the first part of this talk, we study the holonomic system (= a system of differential equations with a finiteness property) M to which the banana Feynman integral is subject. M is a special case of a more general class of D-modules for which we coin the term "reciprocal A-hypergeometric system." We prove that M has holonomic rank (a.k.a. the number of master integrals) 2^{L+1}-1, where L is the number of loops. Moreover, we identify solutions of M with Lauricella's hypergeometric functions F_C. In the second part of the talk, we switch to the general reciprocal A-hypergeometric system. We show that it is a natural matroid analogue of the Gelfand-Kapranov-Zelevinsky theory of A-hypergeometric systems by providing some results: it is holonomic; it has an integral representation; and its singular locus is projectively dual to the reciprocal linear space.The first part is based on joint work in progress with Giacomo Brunello (Scuola Normale Superiore), Vsevolod Chestnov (Oxford), Wojciech Flieger (Padova, OIST), Pierpaolo Mastrolia (Padova), and Nobuki Takayama (Kobe); the second part is based on joint work in progress with Simon Telen (MPI MiS).