A Computational Introduction to the Theory of D-modules

The theory of D-modules is the algebraic theory of systems of linear PDEs. We will discuss the Weyl algebra, and learn how to view PDEs as ideals in this algebra. We will learn about regular holonomic systems and computational techniques to solve them. Our main example will be that of A-hypergeometric systems. If time, we will discuss b-functions, integration of D-modules, and restriction of D-modules.

Date and time info
Monday, 13.00-14.30, last lecture November, 27th

Keywords
D-modules, computation, groebner bases, integrals, A-hypergeometric systems, linear partial differential equations, algebra

Prerequisites
Basic knowledge of rings and ideals is necessary. A student should ideally have taken an introductory ring theory course. Knowledge of Groebner bases in the commutative algebra setting would be helpful but not necessary.