Learning Seminar: Topics in D-modules
This is a learning seminar dedicated to various topics in D-modules. The plan is to start with definitions (the classical and more modern approaches) and basic properties. The participants are encouraged to contribute by selecting a topic from the suggested and presenting it at the seminar, or proposing a topic of their own that is related to the overall theme of the seminar.
Lecturer
Date
8th March ~ 29th June, 2023
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Wednesday | 15:20 - 16:55 | A3-2a-201 | ZOOM 02 | 518 868 7656 | BIMSA |
Prerequisite
Basic concepts of algebraic geometry
Syllabus
The syllabus is not strictly set and can be adjusted based on the interest of the audience. We will start with the following
1. Classical definition of D-modules (via differential operators)
2. Grothendieck's Infinitesimal site
3. Crystals in characteristic p
4. de-Rham stack.
5. Six funtor formalism, Kashiwara equivalence theorem.
6. Singular Support.
7. Holonomic D-modules.
8. Perverse sheaves.
9. Riemann-Hilbert correspondence.
1. Classical definition of D-modules (via differential operators)
2. Grothendieck's Infinitesimal site
3. Crystals in characteristic p
4. de-Rham stack.
5. Six funtor formalism, Kashiwara equivalence theorem.
6. Singular Support.
7. Holonomic D-modules.
8. Perverse sheaves.
9. Riemann-Hilbert correspondence.
Reference
1. Hotta, Takeuchi, Tanisaki. D-modules, Perverse Sheaves and Representation Theory.
2. Bernstein. Algebraic theory of D-modules.
3. Grothendieck. Dix Exposes: Crystals and the de Rham cohomology of Schemes.
4. Berthelot, Ogus. Notes on Crystalline Cohomology.
5. Gaitsgory, Rozenblyum. Crystals and D-modules.
2. Bernstein. Algebraic theory of D-modules.
3. Grothendieck. Dix Exposes: Crystals and the de Rham cohomology of Schemes.
4. Berthelot, Ogus. Notes on Crystalline Cohomology.
5. Gaitsgory, Rozenblyum. Crystals and D-modules.
Audience
Graduate
Video Public
No
Notes Public
No
Language
English
Lecturer Intro
I have MSc degree in Applied Math / Computer Science from St. Petersburg IFMO and PhD in pure mathematics from Yale University. From 2014 to 2022 I held postdoctoral and visiting researcher positions in Japan, UK, Germany and France. I've joined BIMSA in 2023.
My current research interests include geometric representation theory, super groups and non-commutative algebraic geometry.