| Course: | MATH 7364, Topics in Representation Theory |
| Time and place: | Mon., Wed. 2:50 - 4:20pm in 509 Lake Hall |
| Textbook: | not used (the course will be based on instructor's notes and original journal publications) |
| Instructor: | Professor Andrei Zelevinsky |
| Office and phone: | 431 LA, x5648 |
| Email: | andrei (at) neu (dot) edu |
| Office hours: | MWTh. 10:30 - 11:35, or by appointment |
The course gives an introduction to the theory of cluster algebras. This theory is still quite young but it has already found a number of exciting connections and applications: quiver representations, preprojective algebras, Calabi-Yau algebras and categories, Teichmuller theory, discrete integrable systems, Poisson geometry, to name a few. The current state of these developments, including links to papers, working seminars, conferences, etc., is represented at the online Cluster Algebras Portal created and maintained by Sergey Fomin.
The course will cover the foundations of the theory from scratch and is designed to stay elementary and accessible to students without any preliminary knowledge of the subject. We will focus on algebraic and combinatorial aspects of the theory and its algebraic-geometric and Lie-theoretic connections. The prerequisites do not go beyond basic graduate level algebra.
The grading will be based on research projects and/or presentations by students, either during the semester, or more likely, at a mini-conference in the end.
Session 1: Tuesday, December 15, 2:00pm - 5:00pm, in 509 LA
Andrew Carroll: Additive categorification of cluster algebras.
Andrea Appel: Quantum affine algebras and cluster algebras I.
Salvatore Stella: Quantum affine algebras and cluster algebras II.
Yaping Yang: Recognizing cluster algebras of finite type.
Federico Galetto: Grassmannians and cluster algebras.
Gabriel Cunningham: Laurent expansions in rank 2 cluster algebras of affine type.
Jason Ribeiro: Frieze patterns and Markoff numbers.
Florian Kacaku: Nested complexes and graph associahedra.
Ilanit Helfand: Multidimensional cube recurrence.