Introduction to D-Modules (Spring term 2019)
ContentThis lecture aims at giving a leisure introduction to the field of algebraic analysis, that is, the algebraic study of linear partial differential equations with polynomial coefficients. We will start with basics on differential operators and the Weyl algebra as well as on vector bundles with connections. Next we will discuss the notion of holonomicity and how this gives finiteness restrictions on the solutions of a D-module. Depending on time and audience, we will go into some details of direct and inverse images, give the statement of the Riemann-Hilbert correspondence, explain some facts about filtered D-modules as well as on the V-filtration and Bernstein-Sato polynomials. Finally, we may give a small outline on the theory of mixed Hodge modules.
- Ryoshi Hotta, Kiyoshi Takeuchi, Toshiyuki Tanisaki: D-Modules, Perverse Sheaves, and Representation Theory (Chapter 1-8), Birkhäuser
- Chris A.M. Peters, Joseph H.M. Steenbrink: Mixed Hodge Structures (Chapter 13-14), Springer
- Philippe Maisonobe, Claude Sabbah: Aspects of the theory of D-Modules (Lecture notes, on Sabbah's homepage)