Topological Modular Forms
This course is about how different areas of math are linked together. We will start by learning about Kepler's laws of how planets move, then move on to the Atiyah-Singer index theorem and elliptic cohomology, and finally explore topological modular forms. This journey covers many interesting topics like operator theory, modular forms, elliptic curves, string theory, and homotopy theory. The main purpose of this course is to discover and understand different parts of math naturally, following the history of topological modular forms as our guiding theme.
讲师
日期
2024年10月14日 至 12月30日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周一 | 13:30 - 16:55 | A3-3-201 | ZOOM 06 | 537 192 5549 | BIMSA |
修课要求
There are no hard prerequisites for this course. I will try to aim the material at students who have taken first-year graduate courses in algebra, topology, and analysis.
参考资料
1. C. T. C. Wall: Determination of the cobordism ring
2. M. F. Atiyah and I. M. Singer: The index of elliptic operators on compact manifolds
3. F. Hirzebruch: The signature theorem: reminiscences and recreation
4. Edward Witten: Elliptic genera and quantum field theory
5. Edward Witten: The index of the Dirac operator in loop space
6. Michael J. Hopkins: Topological modular forms, the Witten genus, and the theorem of the cube
7. J. V. Armitage and W. F. Eberlein: Elliptic functions
8. Serge Lang: Introduction to modular forms
9. Martin Olsson: Algebraic spaces and stacks
2. M. F. Atiyah and I. M. Singer: The index of elliptic operators on compact manifolds
3. F. Hirzebruch: The signature theorem: reminiscences and recreation
4. Edward Witten: Elliptic genera and quantum field theory
5. Edward Witten: The index of the Dirac operator in loop space
6. Michael J. Hopkins: Topological modular forms, the Witten genus, and the theorem of the cube
7. J. V. Armitage and W. F. Eberlein: Elliptic functions
8. Serge Lang: Introduction to modular forms
9. Martin Olsson: Algebraic spaces and stacks
视频公开
公开
笔记公开
公开
语言
英文
讲师介绍
本科和博士毕业于中国科学技术大学，之前是清华大学丘成桐数学科学中心博士后，现在是北京雁栖湖应用数学研究院助理研究员，研究兴趣是用拓扑方法（cobordism）研究理论物理（anomaly）。