OPAL

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
• S.C. Coutinho: A Primer of Algebraic D-modules, Cambridge University Press

Venue


The lecture will be every Tuesday 13.45-15.15, via Zoom. Some parts will be done in hybrid form. In any case, you can follow the lecture at this

https://us02web.zoom.us/j/88268435457?pwd=ZkgwNkNtMmNXS1VpcS9ubDk2NUY0QT09

Zoom adress. The first lecture is on Tuesday, 5th of April 2022.

Lectures will be recorded, and can be retrieved at this address.

There is a weekly exercise class, every Thursday, 11.30-13.00. The zoom link for the class is

https://us02web.zoom.us/j/6633119403