View source for Reading Seminar on D-modules (2024S)

We meet on Tuesdays at 3pm on Zoom (email arinkin@math.wisc.edu for the link if you need it). The first meeting is on Tuesday, June 25th.

== Tentative schedule ==

{| cellpadding="8"
!align="left" | date
!align="left" | speaker
!align="left" | title 
!align="left" | 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
|Jameson
|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).
|-
|<s>July 9</s> July 16, <b>2:30pm</b>
|Dima 
|Inverse and direct images. Derived category of D-modules
|`Naive' definition. Definition in the derived category (examples).  
|-
|July 23
|Alex
|Kashiwara's Lemma. Integral transforms.
|Kashiwara's Lemma. Tensor product. Integral transforms (=Fourier-Mukai functor). The Fourier-Mukai transform on a line (this is too much for a single talk - topics to be adjusted).
|-
|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
|Kevin 
(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 (or just add to this list)!

* J.Bernstein's [https://gauss.math.yale.edu/~il282/Bernstein_D_mod.pdf 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 [https://gauss.math.yale.edu/~il282/Ginzburg_D_mod.pdf notes]
* C.Schnell's course on D-modules with lecture-by-lecture notes ([https://www.math.stonybrook.edu/~cschnell/mat615/ 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 [https://arxiv.org/abs/1702.03608 paper] by M.Kamgarpour and S.Weatherhog.