中科院数学与系统科学研究院
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（V）
时 间：2024年5月21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 fifth lecture, we will describe silting theory, which is a way to relate the
module categories of two algebras. Here, the second algebra is the endomorphism
algebra of a 2-term silting complex over the first algebra. In particular, when the
first algebra is hereditary, the second one has a nice property.
题 目：Silting theory and cluster theory（VI）
时 间：2024年5月28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 sixth lecture, we will discuss the relationship between the derived categories
of the module categories of two algebras connected by silting theory. More generally,
this relationship can be extended to the Happel-Reiten-Smalø tilting case.
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