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.
讲师
日期
2023年03月08日 至 06月29日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周三 | 15:20 - 16:55 | A3-2a-201 | ZOOM 02 | 518 868 7656 | BIMSA |
修课要求
Basic concepts of algebraic geometry
课程大纲
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.
参考资料
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.
听众
Graduate
视频公开
不公开
笔记公开
不公开
语言
英文
讲师介绍
Slava Pimenov于圣彼得堡IFMO取得应用数学/计算机科学硕士学位，在耶鲁大学取得纯数博士学位。2014年至2022年，他在日本、英国、德国和法国担任博士后和访问研究员，2023年加入BIMSA任助理研究员。他目前的研究兴趣包括几何表示理论、超群和非交换代数几何。