课程题目:Geometric methods in Representation theory

主讲人:林宗柱，堪萨斯州立大学教授

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=MGJDM0N1UHRveVITMk1TazNXQjRpdz09

ZoomlD:94302870352密码:Henu-KSU

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字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 algebras4.Representations of quivers 5. Classiffication of objects in an Abelian category, semisimple case6. Representation Types 7.Grothendieck groups of abellan categories 8. Representations of commutative algebras.

CHAPTER 2.Introduction to algebraic varieties.

1.Affine varieties and algebraic sets 2. Introduction to affne algebraic groups 3. Agebraic group actions on algebraic varieties 4.Quotient varieties 5 Sheaf theory 6.Quasl-coherent sheaves over algebraic algebraic varieties 7. Sheaf cohomology 8. Projectve vareties and flag varieties 9.

Finiteness theorem of sheaf cohomology and Serre duality 10.Borel-Wlil-Theorem for flag varieties.

CHAPTER 3.Schemes and moduli spaces.

1. Ringed spaces 2. Schemes as functors Afine functors representable functors,3.Grothendieck topologles 4.Modull spaces 5. Stacks 6. Coarse modul andfifine modull spaces.