Multivariate Creative Telescoping and Applications to k-regular graphs counting

A central idea in analytic combinatorics is that combinatorial objects can be studied via their generating functions. In many situations, these generating functions admit representations as parametric sums or integrals, which allows one to compute differential equations or recurrences via a method called creative telescoping.

In this talk, I will present a recent algorithm for computing linear differential equations satisfied by multivariate integrals via creative telescoping. The method combines reduction techniques with Gröbner basis computations in Weyl algebras to treat integrals of holonomic functions.

As an application, I will discuss the computation of a differential equation for the generating function of 8-regular graphs, a problem that was previously out of reach. This is joint work with Frédéric Chyzak and Pierre Lairez and is part of my PhD thesis