课程题目：Geometric methods in Representation theory
主讲人：林宗柱教授（堪萨斯州立大学）
课程时间:2020 年 4 月 21 日-6 月 28 日,每周两次课，分别为此时间段每周星期二、星期五晚上 20:00-21:30
课程网址：
https://ksu.zoom.us/j/94302870352?pwd=MGJDM0N1UHRveVlTMk1TazNXQjRpdz09
ZoomID：94302870352 密码:Henu-KSU（以后每次课程ID和密码同此）
课程简介：
本课程主要以表示论中的几何方法为主题，讲授对象为代数及数学物理方向的硕士研究生和高年级本科生，讲授几何和数学物理中的表示论方法和理论。课程主要内容包括如下一些方面:
CHAPTER 1. Introduction to linear representation theory.
1.Representations of groups 2. Representations of algebras 3. Representations of Lie algebras 4. Representations of quivers 5. Classifification of objects in an Abelian category, semisimple case 6. Representation Types 7.Grothendieck groups of abelian categories 8. Representations of commutative algebras.
CHAPTER 2. Introduction to algebraic varieties.
1. Affine varieties and algebraic sets 2. Introduction to affine algebraic groups 3. Algebraic group actions on algebraic varieties 4. Quotient varieties 5 Sheaf theory 6. Quasi-coherent sheaves over algebraic algebraic varieties 7. Sheaf cohomology 8. Projective varieties and flag varieties 9. Finiteness theorem of sheaf cohomology and Serre duality 10. Borel-Weil-Theorem for flag varieties.
CHAPTER 3. Schemes and moduli spaces.
1. Ringed spaces 2. Schemes as functors :Affine functors representable functors.3. Grothendieck topologies 4. Moduli spaces 5. Stacks 6. Coarse moduli and fifine moduli spaces.
敬请有兴趣的老师和学生参加！
