代数拓扑在数据分析中的应用
本课程主要介绍单纯同调理论的基础知识、GLMY同调理论，超图的嵌入同调理论及奇异同调理论，然后结合实际案例，介绍单纯同调和GLMY同调在数据分析中的应用。
讲师
日期
2024年09月10日 至 12月10日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周二,周四 | 10:40 - 12:15 | A3-4-301 | ZOOM 08 | 787 662 9899 | BIMSA |
修课要求
近世代数
课程大纲
1. Homology groups of a simplicial complex.
2. Topological invariance of the homology groups.
3. Relative homology and the Eilenberg-Steenrod Axioms.
4. The GLMY homology of digraphs.
5. The embedded homology of hypergraphs.
6. Persistent Homology.
7. Singular Homology Theory
8. Applications of Homology Theories.
2. Topological invariance of the homology groups.
3. Relative homology and the Eilenberg-Steenrod Axioms.
4. The GLMY homology of digraphs.
5. The embedded homology of hypergraphs.
6. Persistent Homology.
7. Singular Homology Theory
8. Applications of Homology Theories.
参考资料
1. James R. Munkres，Elements of Algebraic Topology.
2. A. Grigor’yan, Y. Lin, Y. Muranov and S.-T. Yau, Homologies of path complexes and digraphs, preprint, 2012. arXiv:1207.2834v4(2013).
3. Jingyan Li，Y. Muranov，Jie Wu and S.-T. Yau, On singular homology theories of digraphs and quivers, Journal of Combinatorics, Priprint.
4. Bressan, Stephane; Li, Jingyan; Ren, Shiquan; Wu, Jie The embedded homology of hypergraphs and applications. Asian J. Math. 23 (2019), no. 3, 479–500.
5. Jingyan Li，Y. Muranov，Jie Wu and S.-T. Yau, On homology of circuits, BJPAM, Priprint.
2. A. Grigor’yan, Y. Lin, Y. Muranov and S.-T. Yau, Homologies of path complexes and digraphs, preprint, 2012. arXiv:1207.2834v4(2013).
3. Jingyan Li，Y. Muranov，Jie Wu and S.-T. Yau, On singular homology theories of digraphs and quivers, Journal of Combinatorics, Priprint.
4. Bressan, Stephane; Li, Jingyan; Ren, Shiquan; Wu, Jie The embedded homology of hypergraphs and applications. Asian J. Math. 23 (2019), no. 3, 479–500.
5. Jingyan Li，Y. Muranov，Jie Wu and S.-T. Yau, On homology of circuits, BJPAM, Priprint.
听众
Undergraduate
, Graduate
视频公开
不公开
笔记公开
不公开
语言
中文
讲师介绍
李京艳，BIMSA助理研究员，2007年获河北师范大学数学系博士学位，先后执教于石家庄铁道大学数理系和河北师范大学数学科学学院，职称副教授，2021年9月入职北京雁栖湖应用数学研究院（BIMSA）。主要研究兴趣在拓扑数据分析和单纯同调与同伦方面。