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.
Lecturer
Date
10th October, 2024 ~ 6th January, 2025
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Monday,Thursday | 09:50 - 11:25 | A3-1-103 | ZOOM 14 | 712 322 9571 | BIMSA |
Prerequisite
Riemannian geometry
Reference
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.
Audience
Undergraduate
, Advanced Undergraduate
, Graduate
, Postdoc
, Researcher
Video Public
No
Notes Public
Yes
Language
Chinese
, English
Lecturer Intro
I am interested in geometric analysis and general relativity. More specifically, I am working on problems related to scalar curvature and geometric problems from physics. I enjoy applying the tools from PDEs, especially elliptic PDEs, to study geometry.