An introduction to Homological Algebra
This is a graduate level course on homological algebra, based on Weibel’s classical textbook. Homological algebra is a tool used in several branches of mathematics, including algebraic topology, commutative algebra and algebraic geometry. We are going to start with the canonical list of subjects (Ext, Tor, etc.). Later, we will focus on some applications to commutative algebra and algebraic geometry.
讲师
日期
2025年02月18日 至 05月20日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周二,周三 | 09:50 - 11:25 | A3-2-201 | ZOOM 01 | 928 682 9093 | BIMSA |
修课要求
An introductory graduate level algebra course should suffice. This means some familiarity with the basic notions of category theory (category, functor, natural transformation) and with the category R-mod (resp. R-mod) of left (resp. right) modules over an associative ring R.
课程大纲
1. Chain complexes
2. Derived functors
3. Tor and Ext
4. Homological dimension
5. Spectral sequences
6. Simplicial methods in homological algebra
7. The derived category
2. Derived functors
3. Tor and Ext
4. Homological dimension
5. Spectral sequences
6. Simplicial methods in homological algebra
7. The derived category
参考资料
1) C. Weibel: An introduction to homological algebra
2) P. Hilton and U. Stammbach: A course in homological algebra
3) H. Cartan and S. Eilenberg: Homological algebra
4) S. Gelfand and Y. Manin: Methods of Homological algebra
2) P. Hilton and U. Stammbach: A course in homological algebra
3) H. Cartan and S. Eilenberg: Homological algebra
4) S. Gelfand and Y. Manin: Methods of Homological algebra
听众
Graduate
视频公开
公开
笔记公开
公开
语言
英文
讲师介绍
Beihui Yuan gained her Ph.D. degree from Cornell University in 2021. She has joined BIMSA in 2023. Her current research interests include application of commutative algebra in pure and applied mathematics problems.