Computational Commutative Algebra
This is a graduate level course on computational commutative algebra. We are going to work on finitely generated graded modules over polynomial rings. The topics include how to compute their combinatorial and homological invariants, e.g. Groebner bases, Hilbert series and betti diagrams. During the course, we are going to work through a lot of examples together via computer algebra system Macaulay2.
讲师
日期
2026年03月03日 至 05月29日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周二,周五 | 15:20 - 16:55 | A3-3-201 | ZOOM 06 | 537 192 5549 | BIMSA |
修课要求
Basic knowledge on rings, ideals, varieties and their correspondence should be sufficient. I am going to review them in the first lecture anyway.
课程大纲
1. Preliminaries: projective spaces, graded rings and modules, chain complexes and homologies.
2. Free resolutions, Betti diagrams and Hilbert functions.
3. Monomial ideals and initial ideals
4. Groebner bases
5. The geometry of syzygies
6. Other related topics
2. Free resolutions, Betti diagrams and Hilbert functions.
3. Monomial ideals and initial ideals
4. Groebner bases
5. The geometry of syzygies
6. Other related topics
参考资料
1) I. Peeva: Graded Syzygies
2) B. Hasset: Introduction to Algebraic Geometry
3) V. Ene and J. Herzog: Groebner basis in Commutative Algebra
4) D. Eisenbud: Commutative Algebra with a View toward algebraic geometry
5) E. Miller and B. Sturmfels: Combinatorial Commutative Algebra
2) B. Hasset: Introduction to Algebraic Geometry
3) V. Ene and J. Herzog: Groebner basis in Commutative Algebra
4) D. Eisenbud: Commutative Algebra with a View toward algebraic geometry
5) E. Miller and B. Sturmfels: Combinatorial Commutative 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.