2025/2026 (Autumn) Topics in Mathematical Science
Course themeQuiver representations and homological
algebras
Preliminary lecture plan
| Week | Date | Topic |
|---|---|---|
| 1 | 10-02 | Overview. Reminders on algebras and modules. |
| 2 | 10-09 | Indecomposablility, Krull-Schmidt, simple, Schur's lemma |
| 3 | 10-16 | Quivers and path algebras and their representations. Duality. Idempotents |
| 4 | 10-23 | Jordan-Hölder, Artin-Wedderburn |
| 5 | 10-30 | Topological Data Analysis, linear matrix pencil. Bound quiver. |
| 6 | 11-06 | -- NO LECTURE -- (Sick Leave) |
| 7 | 11-13 | Bound quiver continued. Basic category theory |
| 8 | 11-20 | Additive and abelian categories. |
| 9 | 11-27 | --- NO LECTURE --- |
| 10 | 12-04 | Bimodule, tensor Hom adjunction, exactness |
| 11 | 12-11 | Exactness (continued), projective, injective |
| 12 | 12-18 | --- NO LECTURE --- |
| 13 | 12-25 | Resolution, Ext, extension, Tor |
| 14 | 01-08 | --- NO LECTURE --- |
| 15 | 01-15 | Morita theory |
| 16 | 01-22 | Tilting theory |
Time and Venue Thursday 13:00–14:30, Grad. School of Mathematics Room 409
Evaluation
- There is no examination. Grading is evaluated through homework assignments.
- In each assignment, the 2 highest scoring question will be recorded.
- Final grading is determined by the average of the 5 highest recorded marks.
- Grading scheme is as follows.
- A : 85 ∼ 100%
- B : 70 ∼ 84%
- C : 50 ∼ 69%
- Fail : 0 ∼ 49%
References (In order of preferences)
- I. Assem, A. Skowronski, D. Simson: Elements of the Representation Theory of Associative Algebras Vol 1. Cambridge University Press 2006
- K. Erdmann and T. Holm: Algebras and representation theory. Springer Undergraduate Mathematics Series, Springer 2018
- M. Auslander, I. Reiten, S.O. Smalo: Representation Theory of Artin Algebras. Cambridge University Press 1995
- A. Zimmermann: Representation Theory: A Homological Algebra Point of View. Springer 2014