MATH6150H - Introduction to Cluster Algebra
Lecture:
| Instructor: | Prof. IP, Ivan Chi Ho |
| Email: | ivan.ip@ust.hk |
| Office: | Room 3483 (Lift 25-26) |
| Office Hour: | by appointment or whenever my office door is open :P |
Class Hour and Venue:
Tuesday Thursday 12:00 - 13:20 @ 5510 (Lift 25-26)
Course Description:
"How do you describe a matrix where the determinant of every submatrix is positive?"
The answer to this simple question has a rich algebraic structure. The theory of Cluster Algebra was introduced in 2000 to study the above problem of total positivity. This new theory quickly becomes one of the most important research areas in mathematics, which finds applications in representation theory, combinatorics, hyperbolic geometry, algebraic geometry, dynamical systems, quantum theory and mathematical physics.
This is an introductory course for graduate and advanced undergraduate students. After treating carefully the basics, we will survey some of the research topics in cluster algebra, covering the required backgrounds, if necessary.
Prerequisites:
Basic concepts of linear algebra, group, ring and module theory.
Grading:
There will be 4 to 5 homework.
References:
- Lecture Notes (by the instructor) (Modules)
- S. Fomin and A. Zelevinsky, Cluster algebras I, II, III, IV
- S. Fomin, L. Williams, and A. Zelevinsky, Introduction to cluster algebras,
Chapters 1-3, Chapter 4-5 - R. Marsh, Lecture Notes on Cluster Algebras.
More references for specific topics can be found in the Bibliography and the Cluster Algebra Portal.
Resources for Abstract Algebra:
Course Summary:
| Date | Details | Due |
|---|---|---|