Dirac Operators and Applications to Scalar Curvature
The Dirac operator is an important tool for studying scalar curvature. We will introduce Dirac operators and the index theorem for Dirac
operators. Following this, we will focus on some applications to positive mass theorems and scalar curvature problems.
operators. Following this, we will focus on some applications to positive mass theorems and scalar curvature problems.
讲师
日期
2024年10月10日 至 2025年01月06日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周一,周四 | 09:50 - 11:25 | A3-1-103 | ZOOM 14 | 712 322 9571 | BIMSA |
修课要求
Riemannian geometry
参考资料
1. H. Blaine Lawson and Marie-Louise Michelsohn, Spin Geometry (PMS-38), Volume 38. Vol. 20. Princeton University Press, 2016.
2. Misha Gromov, Four lectures on scalar curvature, arXiv:1908.10612 (2019).
3. Xianzhe Dai, Lectures on Dirac Operators and Index Theory.
2. Misha Gromov, Four lectures on scalar curvature, arXiv:1908.10612 (2019).
3. Xianzhe Dai, Lectures on Dirac Operators and Index Theory.
听众
Undergraduate
, Advanced Undergraduate
, Graduate
, 博士后
, Researcher
视频公开
不公开
笔记公开
公开
语言
中文
, 英文
讲师介绍
我的研究方向是几何分析和广义相对论，目前主要研究标量曲率和广义相对论中的几何问题。我应用偏微分方程，特别是椭圆方程，来研究几何问题。