Simplicial Homology and GLMY-Homology
本课程从单纯复形的相关概念开始，介绍单纯复形的单纯同调，持续单纯同调和Combinatorial Laplacian；进而介绍了有向图的GLMY同调，超图的嵌入同调以及相应的持续同调和算法、Hodge Laplacian，最后介绍twisted 同调。
讲师
日期
2023年09月19日 至 12月14日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周二,周四 | 13:30 - 15:05 | A3-4-101 | ZOOM 04 | 482 240 1589 | BIMSA |
修课要求
Linear Algebra
课程大纲
1. Simplicial complex.
2. Homology groups of a simplicial complex and topological invariance of the homology groups, persistent homology and Combinatorial Laplacian.
3. The GLMY homology of digraphs, persistent homology and Hodge Laplacian.
4. The embedded homology of hypergraphs.
5. Twisted Homology.
2. Homology groups of a simplicial complex and topological invariance of the homology groups, persistent homology and Combinatorial Laplacian.
3. The GLMY homology of digraphs, persistent homology and Hodge Laplacian.
4. The embedded homology of hypergraphs.
5. Twisted Homology.
参考资料
1. Simplicial Objects and Homotopy Groups, Lecture notes of Jie Wu.
2. Elements of Algebraic Topology，James R. Munkres.
3. A. Grigor’yan, Y. Lin, Y. Muranov and S.-T. Yau, Homologies of path complexes and digraphs, preprint, 2012. arXiv:1207.2834v4(2013).
4. A. Grigor’yan, Y. Lin, Y. Muranov and S.-T. Yau, Cohomology of digraphs and (undirected) graphs, Asian J. Math. 19 (2015),887–932.
5. A. Grigor’yan, Y. Muranov and S.-T. Yau, Graphs associated with simplicial complexes, Homology, Homotopy Appl., 16:1 (2014), pp. 295–311.
6. Bressan, Stephane; Li, Jingyan; Ren, Shiquan; Wu, Jie The embedded homology of hypergraphs and applications. Asian J. Math. 23 (2019), no. 3, 479–500.
2. Elements of Algebraic Topology，James R. Munkres.
3. A. Grigor’yan, Y. Lin, Y. Muranov and S.-T. Yau, Homologies of path complexes and digraphs, preprint, 2012. arXiv:1207.2834v4(2013).
4. A. Grigor’yan, Y. Lin, Y. Muranov and S.-T. Yau, Cohomology of digraphs and (undirected) graphs, Asian J. Math. 19 (2015),887–932.
5. A. Grigor’yan, Y. Muranov and S.-T. Yau, Graphs associated with simplicial complexes, Homology, Homotopy Appl., 16:1 (2014), pp. 295–311.
6. Bressan, Stephane; Li, Jingyan; Ren, Shiquan; Wu, Jie The embedded homology of hypergraphs and applications. Asian J. Math. 23 (2019), no. 3, 479–500.
听众
Undergraduate
, Graduate
视频公开
公开
笔记公开
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。