Georgia Institute of Technology College of Sciences

As a continuation to last week's talk, we introduce the ring D of differential operators with complex coefficients, or the Weyl algebra. As we saw last week, the theory of the ring R, the ring of differential operators with rational function coefficients, is in many ways almost the same as the regular polynomial ring. The ring D however will look slightly different as its structure is much finer. We will look at filtrations, graded rings and Gröbner bases induced by weight vectors. Finally we will present an overview on the integration algorithm of holonomic D-modules and mention some applications.