Dr. Delphine Pol • Prof. Dr. Mathias Schulze
The seminar will cover some basics of D-module theory following the introductory book by Coutinho.
We started with an organizational meeting in the first week. The seminar takes place Thursdays 15:30-17:00 in room 48-436.
To enroll in the seminar please visit the URM.
Initially each participant will be assigned one chapter to present. When everyone has given a talk, we start a second round of talks. Finally everyone will have presented 2 (or at most 3) chapters.
| Meeting | Date | Speaker | Title |
|---|---|---|---|
| 0 | 24.10.2018 | Mathias Schulze | organizational meeting |
| 1 | 8.11.2018 | Firoozeh Aga | The Weyl algebra |
| 2 | 15.11.2018 | Dominik Bendle | Ideal structure of the Weyl algebra |
| 3 | 22.11.2018 | Clara Petrol | Rings of differential operators |
| 4 | 29.11.2018 | Daniel Schaefer | Modules over the Weyl algebra The D-module of an equation |
| 5 | 6.12.2018 | Benjamin Mirgain | Graded and filtered modules |
| 6 | 13.12.2018 | Benjamin Mirgain Firoozeh Aga | Good filtrations The Hilbert polynomial |
| 7 | 10.1.2019 | Firoozeh Aga | Dimension and multiplicity |
| 8 | 17.1.2019 | Firoozeh Aga Dominik Bendle | Bernstein's inequality Holonomic modules |
| 9 | 24.1.2019 | Dominik Bendle Clara Petrol | The Bernstein polynomial Characteristic varieties |
| 10 | 31.1.2019 | Clara Petrol Daniel Schaefer | Symplectic structures and involutivity Tensor products |
| 11 | 7.2.2019 11:45-13:15 | Daniel Schaefer | External products |
| 12 | 7.2.2019 | Benjamin Mirgain | Inverse images |
You need to make two appointments to meet with Dr. Pol in the course of preparing your talk. If you have problems understanding the material please contact us immediately.
After reading the assigned literature you create a plan for your talk. Define the goal(s) of your talk. Which definitions, ideas and results do you want to present? How do you structure the talk? Which results are worth proving them in full details? Which results you just formulate as a black-box? Which ideas do you explain? Which examples best illustrate the material? How much time do you schedule for each item? In a first meeting with Dr. Pol you discuss your plan and get recommendations on how to modify it.
Based on your plan you create a detailed draft of your talk. In a second meeting with Dr. Pol you present and discuss this draft. The final draft may serve as a hand-out for the participants.
To gain credit points you need to give a good talk.
S. C. Coutinho: A Primer of Algebraic D-Modules, LMS Student Texts 33, Cambridge University Press, 1995.