Computational Commutative Algebra
This is a graduate level course on computational commutative algebra. The central theme in this course is the study of (finite) free resolutions, which provides a lot of invariants for graded modules. We are going to learn tools to study and computes free resolutions, as well as using free resolution as a tool to study geometry of projective varieties. During the course, we are going to work through a lot of examples together. The audience are strongly encouraged to generate their own examples and test their ideas with computer algebra systems, e.g. CoCoA, Singular and Macaulay2.
讲师
日期
2024年02月27日 至 05月16日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周二,周四 | 09:45 - 11:50 | A3-4-312 | ZOOM 01 | 928 682 9093 | BIMSA |
修课要求
A first course in commutative algebra and algebraic geometry. Basic knowledge on rings, ideals and varieties should be sufficient.
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) H. Schenck: Computational Algebraic Geometry
3) D. Eisenbud: The Geometry of Syzygies
4) D. Eisenbud: Commutative Algebra with a View toward algebraic geometry
5) E. Miller and B. Sturmfels: Combinatorial Commutative Algebra
2) H. Schenck: Computational Algebraic Geometry
3) D. Eisenbud: The Geometry of Syzygies
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.