D-modules

Lectures: Tuesday 09.00-11.00, 7th October - 9th December. 

For those not at the University of Glasgow, the lectures are via the usual SMSTC Zoom link. For those at the University of Glasgow, lectures are in TBA. 

D-modules play a central role in representation theory and an important role in many aspects of algebraic geometry. This course, which assumes only a basic knowledge of algebraic geometry, will develop from scratch the theory of D-modules.

The end goal of the course is to understand the statement of the Riemann-Hilbert correspondence, giving an equivalence between the category of regular holonomic D-modules and the category of perverse sheaves (with complex coefficients) on a smooth complex algebraic variety.

Topics covered in the build-up to the equivalence include push-forward and pull-back of D-modules, good filtrations and characteristic varieties, holonomic D-modules, duality for holonomic D-modules and the classification of simple holonomic D-modules via minimal extensions.  

For those who require a grade from this course, there will be two assessments. These are group assessments, meaning you are strongly encouraged to work in groups to solve the problems - you should submit individual write-ups of the solution to the SMSTC website. 

• Assessment 1; released noon on November 4th, due at 23:59 on the 18th November.

• Assessment 2; released noon on December 9th, due at 23:59 on the 6th January 2026.

Each assessment will count 50% towards the final grade.

I will also provide 5 exercise sheets and offer an office hour on Zoom for anyone who has questions, or wants to discuss any aspect of the course. These will be weekly, 3pm on Tuesday, from 14th October. 

Lecture notes and exercises will appear here in due course.