Introduction to combinatorial homotopy theory
This course aims to help the students whose future research plan would be in studying homotopy theory or applying the techniques of homotopy theory in their areas. The course will intensively discuss some important notions in homotopy theory using combinatorial approaches, aiming to established the fundamental connections between the modular representation theory and the homotopy theory of the loop-suspension functor. The course will discuss functorial decompositions of some basic constructions in homotopy theory such as self-smashes and the loop-suspensions using representation theory and combinatorial group approaches, with concentrating on the homotopy theory of concrete examples of finite complexes, so that the students may apply the techniques learned from the course to the homotopy theory of more abstract categories in their future development.
讲师
日期
2026年09月21日 至 2027年01月15日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周五 | 14:20 - 16:55 | Shuimo | ZOOM 01 | 928 682 9093 | BIMSA |
修课要求
Algebraic Topology
课程大纲
H-spaces and co-H-spaces, Geometric representation of symmetric groups and homotopy decompositions of self-smashes, Hopf algebra; James construction, Whitehead products, Samelson products, Cohen group, natural self-transformations of the loop suspension functor, functor A^{min} , functor B^{max}，functor Q^{max}，homotopy decompositions of loops on co-H-spaces; EHP sequences and homotopy groups.
参考资料
1. Selick, Paul; Wu, Jie, On natural coalgebra decompositions of tensor algebras and loop suspensions, Mem. Amer. Math. Soc. 148, no. 701, viii+109 pp.(2000).
2. Jie Wu, Homotopy theory of the suspensions of the projective plane, Mem. Amer. Math. Soc. , 162(769), x+130pp. (2003)
3. Jie Wu, On maps from loop suspensions to loop spaces and the shuffle relations on the Cohen groups, Mem. Amer. Math. Soc. 180, no. 851, vi+64 pp.(2006)
2. Jie Wu, Homotopy theory of the suspensions of the projective plane, Mem. Amer. Math. Soc. , 162(769), x+130pp. (2003)
3. Jie Wu, On maps from loop suspensions to loop spaces and the shuffle relations on the Cohen groups, Mem. Amer. Math. Soc. 180, no. 851, vi+64 pp.(2006)
听众
Advanced Undergraduate
, Graduate
视频公开
公开
笔记公开
公开
语言
中文
讲师介绍
BIMSA研究员，美国罗切斯特大学数学系博士，加州大学伯克利分校数学研究所博士后，前新加坡国立大学数学系终身教授，2021年12月入职北京雁栖湖应用数学研究院（BIMSA）。研究方向为代数拓扑与应用拓扑，在代数拓扑理论研究上的主要成就是建立了同伦群与辫子群理论的基础性关系，以及回路空间同伦论与置换群模表示论的基础性关系；在应用拓扑方面，他带领研究团队以复杂系统高阶互作拓扑基础为目标、生物医学与材料科学等领域科学问题为导向，发展有向图与超图的代数拓扑学，推动拓扑数据分析的新型拓扑理论及其应用，取得了一系列成果。在Journal of American Mathematical Society, Proceedings of the National Academy of Sciences of the United States of America, Advances in Mathematics等数学顶尖期刊发表学术论文100余篇。2007年获得新加坡国家科学奖。2014年获得国家自然科学基金海外联合基金（杰青B）的资助