The purpose of the course is to give an introduction to the theory of D-modules, i.e. modules over algebras of linear differential operators. We will be particularly interested in its applications to representation theory.
Tentative plan: - (Sheaves of) algebras of differential operators; - D-modules (singular support, characteristic cycles, holonomicity); - constructible sheaves, statement of Riemann-Hilbert correspondence; - functoriality (pullback and pushforward, Kashiwara's lemma); - Verdier duality, preservation of holonomicity; - equivariant and twisted D-modules, BeÄlinson-Bernstein theorem.
Textbook: R. Hotta, K. Takeuchi, T. Tanisaki, D-modules, perverse sheaves and representation theory. Progress in Mathematics, 236. Birkhauser, 2008
Target group: scientists interested in algebraic geometry and representation theory.
Prerequisites: Knowledge of basic algebraic geometry (First three chapters of Hartshorne). Familiarity with representation theory of algebraic groups is desirable for later parts, but not required.
Evaluation: Biweekly homework, student presentations as final exam
Teaching format: Lectures
ECTS: 6 Year: 2020
Track segment(s):
MAT-ALG Mathematics - Algebra
MAT-GEO Mathematics - Geometry and Topology
Teacher(s):
Quoc Ho Sasha Minets
Teaching assistant(s):
If you want to enroll to this course, please click: REGISTER
- Teacher: Quoc HO
- Teacher: Alexandre MINETS