TCC course: D-modules

Wednesdays, 2pm-4pm, starting 16/01/2019.

Lectures take place in whichever room your department uses for video lectures. In Oxford, this is VC.

There is no lecture on 27/02. Instead we'll have an extra lecture on 13/03.

Lecture notes

Will be posted here.

Course syllabus

D-modules are modules over the sheaf of differential operators on an algebraic variety (or scheme, or manifold, ...).
They give one of the most fundamental instances of non-commutative algebra entering algebraic geometry.
We will develop the basic language of D-modules and see how it connects with areas like differential equations and in particular representation theory.
The final goal of the course is the Riemann-Hilbert correspondence, which shows that a category of D-modules encodes topological information about the underlying space: the category of regular holonomic D-modules on X is equivalent to the categories of perverse sheaves on X.

Preliminaries

Good knowledge of basic algebraic geometry (complex algebraic varieties, basic operations on O-modules).

Familiarity with the language of derived categories is useful, but all notions will be recalled in lectures.

References

The course essentially covers the first half (chapters 1-8) of HTT.

Exercises

Assessment

If you need any form of assessment/credit for this course, please contact me.
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