id=1220
Program
An introduction to cluster categories
Student No.:40
Time:Mon&Tue, 9:50-11:25
Instructor:Zhou Yu  
Place:Conference Room 1,Jin Chun Yuan West Bldg.
Starting Date:2019-2-25
Ending Date:2019-5-17

Description:
In this course, we introduce the categorical aspect of the theory of cluster algebras. We will first review basic knowledge of representation theory of algebras: representations of quivers, tilting theory, derived categories. Then we discuss various topics, including cluster categories, quivers with potential, Ginzburg dg algebras, 3-Calabi-Yau derived categories. As interesting applications, we will apply the above to the surface case.


Prerequisite:
Basic knowledge on representation theory of algebras is helpful.


Reference:
1. Two books for basic knowledge of representation theory of algebra: I. Assem, D. Simson, and A. Skowronski, Elements of the representation theory of associative algebras, vol. 65, Cambridge University Press, Cambridge, 2006; Triangulated categories in the representation of finite dimensional algebras,Cambridge Univ. Press, Cambridge, 1988.
2. Some publications for topics: Tilting theory and cluster combinatorics; Quivers with potentials and their representations I: Mutations; Derived equivalences from mutations of quivers with potential; Cluster categories for marked surfaces: punctured case; and so on.