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

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.

Basic knowledge on representation theory of algebras is helpful.

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.