Introduction to D-modules
Content
This lecture is the follow-up from the spring term's "Introduction to D-modules" class. It 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.
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
- S.C. Coutinho: A Primer of Algebraic D-modules, Cambridge University Press
Venue
The lecture will be every Wednesday 13.45-15.15. It will take place in hybrid form, in room 2/39 633 and via Zoom at
https://us02web.zoom.us/j/85404846945?pwd=S1NkNDJhZEhuUjNPdTZpZlZidFBrUT09
The first lecture is on Wednesday, 12th of October 2022.
Lectures will be recorded, and can be retrieved at this address.
There is a weekly exercise class, every Monday, 9:15-10:45. The zoom link for the class is
https://us02web.zoom.us/j/6633119403