Reading Seminar on D-modules (2024S)

We meet on Tuesdays on Zoom (email arinkin@math.wisc.edu for the link if you need it). The first meeting is on Tuesday, June 25th.

Tentative schedule

date	speaker	title	topics
June 25	Josh	Differential operators and filtrations	We'll define the ring of algebraic differential operators together with its order filtration, and discuss some of its implications for modules over rings of differential operators.
July 2	available	Left and right D-modules. Inverse images	Examples of D-modules on a line. Quasicoherent D-modules. Left vs. right D-modules: an equivalence. Inverse images of D-modules. Examples (open embeddings, smooth morphisms, closed embeddings).
July 9	available (This may be hard to understand from references, so only take this if you are comfortable; otherwise I'll do it. Dima.)	Direct images. Derived category of D-modules	`Naive' definition. Definition in the derived category (examples). Time permitting - Kashiwara's Lemma.
July 16	available	Integral transforms.	Tensor product. Integral transforms (=Fourier-Mukai functor). The Fourier-Mukai transform on a line.
TBD	available	Levelt-Turritin classification	D-modules on punctured formal disk. Regular and irregular singularities. Extra topics: monodromy, the Stokes phenomenon, perhaps some discussion of non-punctured disk
TBD	available (Another big topic)	Holonomic D-modules	Singular support, Bernstein's inequality. Duality for holonomic D-modules
TBD	available	The six functors	Preservation of holonomicity. Functoriality of singular support (?).} References If you have other suggestions, please let me know! J.Bernstein's notes on D-modules. They are quite informal and move very fast. R.Hotta, K.Takeuchi, T.Tanisaki, D-modules, perverse sheaves, and representation theory. Very detailed and carefully written book. V.Ginzburg's notes C.Schnell's course on D-modules with lecture-by-lecture notes (Course page). S.C.Coutinho, A primer of algebraic D-modules. The book does go too deep into theory, focusing instead on examples and practical calculation. For modern approach to Levelt-Turritin classification, here's a paper by M.Kamgarpour and S.Weatherhog.