清华主页 EN
导航菜单

Fibre Bundle Theory

来源: 09-09

时间: 13:30 - 15:05, Mon,Wed, 9/14/2022 - 12/12/2022

地点:Venue: 1118 Zoom: 242 742 6089 PW: BIMSA

主讲人:Jingyan Li (Assistant Research Fellow)

Record: No

Level: Graduate

Language: Chinese


Prerequisite

Simplicial complex theory and simplicial set theory.


Abstract

The notion of fibre bundle first arose out of questions posed in the 1930s on the topology and geometry of manifolds. By the year 1950, the definition of fibre bundle had been clearly formulated, the homotopy classification of fibre bundles achieved, and the theory of characteristic classes of fibre bundles developed by several mathematicians: Chern, Pontrjagin, Stiefel, and Whitney. Fiber bundle theory is not only important in topology and differential geometry, but also is widely used in other branches of mathematics and physics. This course mainly introduces some basic concepts of fiber bundles and the application of fiber bundles in homology theory in comparison with the geometric level and the simple level.


Reference

1. Dale Husemoler, Fibre Bundles.

2. Simplicial Objects and Homotopy Groups, Lecture notes of Jie Wu.

3. Barratt, M. G., Gugenheim, V. K. A. M., and Moore, J. C., On semisimplicial fifibre-bundles, Am. J. Math., 81(3), 1959, 639-657.

4. Curtis, E. B., Simplicial homotopy theory, Adv. Math., 6(2), 1971, 107-209.


Syllabus

Generalities on Bundles, Vector Bundles, General Fibre Bundles, Principal Bundle and the Universal Principal Bundle, Grassmann Manifolds and the Classical Groups, Stability of the Homotopy Groups of the Classical Groups, Universal Bundles and Classifying Spaces for the Classical GroupsSimplicial fibre bundle theory.


Lecturer Intro

Assistant Reserch fellow Jingyan Li received a PhD degree from the Department of Mathematics of Hebei Normal University in 2007. Before joining BIMSA in September 2021, she has taught in the Department of Mathematics and Physics of Shijiazhuang Railway University and the School of Mathematical Sciences of Hebei Normal University as an associate professor. Her research interests include topology data analysis and simplicial homology and homotopy.


Lecturer Email: jingyanli@bimsa.cn

TA: Dr. Zhuo Liu, liuzhuo@bimsa.cn


返回顶部
相关文章
  • Seminar on KSBA Moduli Theory

    Upcoming talks:Families of Varieties of General TypeReference:Ja´nos Koll´ar, Families of varieties of general type, 2022. Chapter 1 ∼ 8.Schedules:Lecture 1 (Sep 22, 2022): History of moduli problems.Lecture 2-3: One-parameter families.Lecture 4: Families of stable varieties.Lecture 5-6: Stable pairs over reduced base schemes.Lecture 7-8: Numerical flatness and stability criteria.Lecture 9-10...

  • MSP theory and BCOV Feynman rule

    Abstract:In 1993, Bershadsky, Cecotti, Ooguri and Vafa predicted a Feynman structure governing the topological string theory of a compact Calabi Yau threefold. In 2006 Yamaguchi and Yau made the BCOV prediction for quintic threefold more explicit, and deduce structural relations from it.In 2018 both predictions were verified for quintic's Gromov Witten theory via the study of Mixed Spin P (MSP...