Comparison Geometry

Speaker：Zhifei Zhu 朱知非

Zhifei Zhu is an Assistant Professor at YMSC. He was a Postdoctoral Fellow at YMSC from 2021 to 2024 and received his Ph.D. from the University of Toronto in 2019. His research focuses on differential geometry, general relativity, and quantitative topology. Dr. Zhu has received the International Postdoctoral Exchange Program Fellowship, CPSF General and Special Programs, CMS Graduate Scholarship, Blyth Fellowship, etc.. He has published in journals such as JDG, JGA, and JMP, and serves as an editor for ICCM Notices.

Time：

Tues. & Thur., 9:50-11:25 am,

Sept. 24-Dec.19, 2024

Venue：

B626, Shuangqing Complex Building A

Description:

This course will explore various comparison theorems, such as the Rauch and Toponogov comparisons, along with their applications. Topics include the Bishop-Gromov volume comparison, sphere theorems, manifold with negative and nonnegative curvature, Gromoll-Meyer splitting theorem, and Cheeger-Gromoll soul theorem.

Prerequisite:

Differential Geometry I

Differential Geometry II

Reference:

1. Comparison Theorems in Riemannian Geometry by Jeff Cheeger, David G. Ebin (available at https://www.ams.org/books/chel/365/chel365-endmatter.pdf)

2. An invitation to Alexandrov geometry: CAT(0) spaces by Stephanie Alexander, Vitali Kapovitch and Anton Petrunin; (available at https://anton-petrunin.github.io/invitation/)

Target Audience:

Undergraduate students, Graduate students

Teaching Language: English