表示论研讨班

数学研究所

学术报告

表示论研讨班

报告人: 周宇教授（清华大学）   

题  目：Silting theory and cluster theory（VII）
    

时  间：2024年6月4日星期二上午 9:00-10:00
   

地  点：S817

摘  要：Cluster algebras were introduced by Fomin and Zelevinsky around 2000. Over the last

 twenty years, the cluster phenomenon was spotted in various areas in mathematics, as well as in 

physics, including combinatorics, commutative and non-commutative algebraic geometry, and the

 representation theory of quivers and finite-dimensional algebras. In this series of lectures, I will

 focus on the new developments in algebraic representation theory inspired by cluster theory, 

particularly silting theory and its applications.
   

In the seventh lecture, we will focus on general silting complexes in the derived category and discuss

their relationships with other important structures in the derived category, such as t-structures and 

co-t-structures. Furthermore, in the case of 2-terms, we will introduce a generalized notion of 

cotorsion pairs in the module category accordingly.
    

题  目：Silting theory and cluster theory（VIII）
    

时  间：2024年6月11日星期二上午 9:00-10:00
   

地  点：S817

摘  要：Cluster algebras were introduced by Fomin and Zelevinsky around 2000. Over the last

 twenty years, the cluster phenomenon was spotted in various areas in mathematics, as well as in 

physics, including combinatorics, commutative and non-commutative algebraic geometry, and 

the representation theory of quivers and finite-dimensional algebras. In this series of lectures, I

 will focus on the new developments in algebraic representation theory inspired by cluster theory, 

particularly silting theory and its applications.
   

In the eighth lecture, I will illustrate with an example how to use geometric models of the derived 

categories of certain finite-dimensional algebras to investigate complementation problems in silting 

theory. These geometric models, also arising from the cluster theory, represent another significant 

contribution of cluster theory to the development of algebraic representation theory.
    

题  目：Silting theory and cluster theory（IX）
    

时  间：2024年6月18日星期二上午 9:00-10:00
   

地  点：S817

摘  要：Cluster algebras were introduced by Fomin and Zelevinsky around 2000. Over the last

 twenty years, the cluster phenomenon was spotted in various areas in mathematics, as well as in 

physics, including combinatorics, commutative and non-commutative algebraic geometry, and the 

representation theory of quivers and finite-dimensional algebras. In this series of lectures, I will 

focus on the new developments in algebraic representation theory inspired by cluster theory, 

particularly silting theory and its applications.
   

In the ninth lecture, I will systematically introduce how the geometric aspects of cluster theory have

 led to geometric models for several categories in algebraic representation theory, and how these 

models are applied to study some important problems in algebraic representation theory.