1. An Introduction to Gauge Theory
授课教师：何思奇，Stony Brook University
课程时间：2020/7/20-2020/8/21 每周二和周四 上午9：00-11：00
课程地点：腾讯会议（ID: 303 737 053)
课程介绍: Mathematical gauge theory is the study of elliptic partial differential equations comes from physics, which are invariant under the action of a group of bundle automorphism. In this mini course, we will in particular talk about mathematical side of the Yang-Mills equations and its interaction with four manifold.
课程安排：共十次课，每次两小时。
The first part of the course will briefly introduce some background on differential manifold, including the theory of bundles and connections, Chern-Weil theory, elliptic operator and elliptic estimates.
The second part of the course will talk about the Yang-Mills equations. We discuss some basic tools in study the moduli space of gauge theory equations. We will sketch the proof of the Uhlenbeck compactness theorem, ADHM construction and Donaldson diagonalization theorem.
参考资料：
[1] Freed and Uhlenbeck, Instantons and Four Manifold
[2] Donaldson and Kronheimer, Geometry of Four Manifold
本课程面向高年级本科生，研究生和青年数学工作者。
预备知识: 微分流形。
主讲人介绍: Siqi He is currently a postdoc at Simons Center of Geometry and Physics in Stony Brook University. He mainly focus on different kind of gauge theory equations, including the Kapustin-Witten equations, the Hitchin-Simpson equations.
视频回放：
Lecture 1-Gauge theory.mp4 Lecture 2-Gauge theory.mp4
Lecture 3-Gauge theory(Part 1).mp4 Lecture 3-Gauge theory(Part 2).mp4
Lecture 4-Gauge theory(Part 1).mp4 Lecture 4-Gauge theory(Part 2).mp4
Lecture 5-Gauge theory(Part 1).mp4 Lecture 5-Gauge theory(Part 2).mp4
Lecture 6-Gauge theory(Part 1).mp4 Lecture 6-Gauge theory(Part 2).mp4
Lecture 7-Gauge theory(Part 1).mp4 Lecture 7-Gauge theory(Part 2).mp4
Lecture 8-Gauge theory(Part 1).mp4 Lecture 8-Gauge theory(Part 2).mp4
Lecture 9-Gauge theory(Part 1).mp4 Lecture 9-Gauge theory(Part 2).mp4
Lecture 10-Gauge theory(Part 1).mp4. Lecture 10-Gauge theory(Part 2).mp4
讲义：
Lecture 1-Gauge theory.pdf Lecture 2-Gauge theory.pdf Lecture 3-Gauge theory.pdf
Lecture 4-Gauge theory.pdf Lecture 5-Gauge theory.pdf Lecture 6-Gauge theory.pdf
Lecture 7-Gauge theory.pdf Lecture 8-Gauge theory.pdf Lecture 9-Gauge theory.pdf
作业：HW 1-Gauge theory.pdf HW2-Gauge theory.pdf HW3-Gauge theory.pdf
百度网盘链接 （密码: d13p）
2. Teichmüller空间简介
授课教师：苏伟旭，复旦大学
课程时间：2020/7/20-2020/7/31 每周一和周三 上午9:00-11:00
课程地点：腾讯会议（ID: 986 568 112）
课程简介: 作为黎曼曲面Teichmüller空间的入门短课,介绍Teichmüller空间的基本知识.主要内容包括: Teichmüller空间的定义; Fenchel-Nielsen坐标; Teichmüller映射; Teichmüller空间的复结构; Teichmüller测地流及其应用。
课程安排: 共四次课,每次两小时，内容依次为:
1) Teichmüller空间的定义,双曲几何, Fenchel-Nielsen坐标。
2) 全纯二次微分; Teichmüller映射; Teichmüller度量。
3) Bers嵌入; Bers同时单值化; Weil-Petersson度量。
4) Teichmüller 测地流; Teichmüller圆盘; Veech曲面。
参考资料:
[1] Ahlfors, Lectures on Quasiconformal Mappings (University Lecture Series). AMS, 2006.
[2] Hubbard, Teichmuller theory and Application to Geometry, Topology and Dynamics. Vol.1 Teichmuller theory.
本课程面向高年级本科生，研究生和青年数学工作者。
预备知识: 复变函数; 黎曼曲面。
主讲人介绍: 苏伟旭, 复旦大学副研究员, 从事Teichmüller空间及其相关领域的研究。
视频回放：Lecture 1-Teichmuller空间.mp4
Lecture 2-Teichmuller空间(Part 1).mp4 Lecture 2-Teichmuller空间(Part 2).mp4 Lecture 3-Teichmuller空间.mp4
Lecture 4-Teichmulelr空间(Part 1).mp4 Lecture 4-Teichmuller空间(Part 2).mp4
讲义：Lecture 1-Teichmuller空间.pdf Lecture 2-Teichmuller空间.pdf Lecture 3-Teichmuller空间.pdf
百度网盘链接（密码: j0je
组织者：李琼玲，南开大学陈省身数学研究所，特聘研究员，qiongling.li@nankai.edu.cn