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 （III）
时 间：2024.05.07（星期二）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 third lecture, I will demonstrate through examples how to mutate support tau-tilting
modules and how to link them with the partially ordered set formed by functorially finite
torsion pairs. We will also explain how such mutations are realized through approximations
and exchange exact sequences.
题 目：Silting theory and cluster theory （IV）
时 间：2024.05.14（星期二）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 fourth lecture, I will explain why tau-tilting theory not only completes tilting theory
from the perspective of mutations but also from the perspective of establishing connections
between the module categories of two algebras, which is the most important application of
tilting theory. For this purpose, we will also discuss the significant role that silting theory
plays in this context.
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