Border bases in the Rational Weyl algebra - with an application to the sunrise integral

In this talk we will introduce border bases - a generalization of Gröbner bases - for a noncommutative ring of differential operators. In the context of Feynman integrals, these border bases will consist of differential operators that annihilate a given Feynman integral. We can obtain such border bases from the 1st order linear PDEs Feynman integrals satisfy (i.e. their differential equations). This method returns an ideal of annihilating differential operators that is "big enough," i.e. of finite holonomic rank.