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About
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Governance
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Visit
People
Management
Faculty
Postdocs
Visiting Scholars
Staff
Administration
Academic Support
Research
Research Groups
Courses
Seminars
Join Us
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Qiuzhen College, Tsinghua University
Yau Mathematical Sciences Center, Tsinghua University (YMSC)
Tsinghua Sanya International  Mathematics Forum (TSIMF)
Shanghai Institute for Mathematics and  Interdisciplinary Sciences (SIMIS)
BIMSA > Selected topics in geometric analysis Ⅰ
Selected topics in geometric analysis Ⅰ
This course is divided into two main topics. The first centres around the introduction of the Ricci flow. The second aims to prove the differentiable sphere theorem.
Lecturer
Liang Di Zhang
Date
27th February ~ 28th May, 2024
Location
Weekday Time Venue Online ID Password
Tuesday,Thursday 15:20 - 16:55 Shuangqing-B534 ZOOM 05 293 812 9202 BIMSA
Prerequisite
Basic knowledge on Riemannian geometry and PDE.
Syllabus
1. Preliminaries: curvatures on Riemannian manifolds
2. Existence and uniqueness of the Ricci flow.
3. Hamilton’s maximum principle
4. Hamilton’s classic results in dimensions 2, 3 and 4
5. Differentiable sphere theorem
Reference
[1] B. Andrews, C. Hopper, The Ricci flow in Riemannian geometry: a complete proof of the differentiable 1/4-pinching sphere theorem, Lecture Notes in Mathematics, Springer, Heidelberg, (2011).
[2] C. Böhm, B. Wilking, Manifolds with positive curvature operator are space forms, Ann. of Math. 167 (2008) 1079-1097.
[3] S. Brendle, R. M. Schoen, Manifolds with 1/4-pinched curvature are space forms, J. Amer. Math. Soc. 22(1) (2009) 287-307.
[4] S. Brendle, Ricci flow and the sphere theorem, Graduate Studies in Mathematics, AMS Press, (2010).
[5] D. DeTurck, Deforming metrics in the direction of their Ricci tensors, J. Differ. Geom. 18 (1983) 157-162.
[6] R. S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differ. Geom. 17 (1982) 255-306.
[7] R. S. Hamilton, Four-manifolds with positive curvature operator, J. Differ. Geom. 24 (1986) 153-179.
[8] R. S. Hamilton, The Ricci flow on surfaces, Contemp. Math. 71 (1988) 237-261.
[9] W. X. Shi, Deforming the metric on complete Riemannian manifolds, J. Differ. Geom. 30 (1989) 223-301.
Audience
Undergraduate , Advanced Undergraduate , Graduate
Video Public
No
Notes Public
Yes
Language
Chinese
Lecturer Intro
Liangdi Zhang received his Ph.D. degree from Zhejiang University in June 2021. He worked as a postdoc at Beijing Institute of Mathematical Sciences and Applications (BIMSA) and Tsinghua University from August 2021 to August 2023. He is currently an assistant professor at BIMSA. His research interests include differential geometry and geometric analysis.
Beijing Institute of Mathematical Sciences and Applications
CONTACT

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北京雁栖湖应用数学研究院 101408

Tel. 010-60661855 Tel. 010-60661855
Email. administration@bimsa.cn

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