Introduction to D-Modules (Spring term 2022)

Content

This 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. 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. This lecture is to be continued in fall 2022.

Literature

Christian Schnell: Algebraic D-modules (graduate course), Lecture notes
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

Venue

The lecture will be hold in hybrid form. You can always follow it via Zoom. To get the Zoom link, please register at the corresponding OPAL page which also gives you access to all necessary information to participate.