TU Kaiserslautern • Department of Mathematics • Winter 2018/9

Seminar «Topics in Algebra and Geometry»

Dr. Delphine PolProf. 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.


024.10.2018Mathias Schulzeorganizational meeting
18.11.2018Firoozeh AgaThe Weyl algebra
215.11.2018Dominik BendleIdeal structure of the Weyl algebra
322.11.2018Clara PetrolRings of differential operators
429.11.2018Daniel SchaeferModules over the Weyl algebra
The D-module of an equation
56.12.2018Benjamin MirgainGraded and filtered modules
613.12.2018Benjamin Mirgain
Firoozeh Aga
Good filtrations
The Hilbert polynomial
710.1.2019Firoozeh AgaDimension and multiplicity
817.1.2019Firoozeh Aga
Dominik Bendle
Bernstein's inequality
Holonomic modules
924.1.2019Dominik Bendle
Clara Petrol
The Bernstein polynomial
Characteristic varieties
1031.1.2019Clara Petrol
Daniel Schaefer
Symplectic structures and involutivity
Tensor products
Daniel SchaeferExternal products
127.2.2019Benjamin MirgainInverse 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.

Credit Points

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.

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