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.
Lecturer
Date
18th February ~ 20th May, 2025
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Tuesday,Wednesday | 09:50 - 11:25 | A3-2-201 | ZOOM 01 | 928 682 9093 | BIMSA |
Prerequisite
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.
Syllabus
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
Reference
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
Audience
Graduate
Video Public
Yes
Notes Public
Yes
Language
English
Lecturer Intro
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.