线上课程Short course：A Retrospective Look at Ricci Flow

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：Bennett Chow (University of California, San Diego)
：2023-03-20 ——2023-03-30
：Tencent Meeting ID： 86966997109 (password:0323)

1. 授课专家 Instructor

Professor Bennett Chow (University of California, San Diego)

2. 短课程介绍 Introduction

Title: A Retrospective Look at Ricci Flow

Abstract: We will discuss aspects of the Ricci flow including the Ricci flow approach to the uniformization of compact surfaces, Hamilton’s classification of 3-dimensional compact manifolds with positive Ricci curvature, Ricci solitons---which are prototypical singularity models for the Ricci flow, statement of the classification of 3-dimensional singularity models, and an introduction to the study of higher-dimensional singularity formation.

References:

Bamler, R. H. Recent developments in Ricci flows. Notices Amer. Math. Soc. 68, 9 (2021), 1486–1498.

Brendle, S. Ricci flow and the sphere theorem, vol. 111 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2010.

Hamilton, R. S. The formation of singularities in the Ricci flow. In Surveys in differential geometry, Vol. II (Cambridge, MA, 1993). Int. Press, Cambridge, MA, 1995, pp. 7–136.

Kleiner, B., and Lott, J. Notes on Perelman’s papers. Geom. Topol. 12, 5 (2008), 2587–2855.

Morgan, J., and Tian, G. Ricci flow and the Poincaré conjecture, vol. 3 of Clay Mathematics Monographs. American Mathematical Society, Providence, RI; Clay Mathematics Institute, Cambridge, MA, 2007.

Perelman, G. The entropy formula for the Ricci flow and its geometric applications. arXiv:math.DG/0211159.

Topping, P. Lectures on the Ricci flow, vol. 325 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge, 2006.

3. 授课时间与内容 Schedule and Summary of Topics

Beijing Time

Summary of topics

March 20 Mon

8:00-9:30 AM

Lecture 1：Ricci Flow on Surfaces

References: Bennett Chow and Dan Knopf, Ricci Flow: An Introduction, Chapter 5, AMS 2004;

Bennett Chow and Yutze Chow, Lectures on Differential Geometry, Chapter 14, in preparation.

March 23 Thu

8:00-9:30 AM

Lecture 2: Three-Manifolds with Positive Ricci Curvature

Reference: Bennett Chow, Peng Lu, and Lei Ni, Hamilton’s Ricci flow, Chapter 3, AMS 2006.

March 25 Sat

8:00-9:30 AM

Lecture 3: Ricci Solitons

Reference: Bennett Chow, Ricci Solitons in Low Dimensions, AMS, to appear.

March 27 Mon

8:00-9:30 AM

Lecture 4: 3-Dimensional Singularity Models

Reference: Hamilton, R. S. The formation of singularities in the Ricci flow. JDG 1995.

Perelman, G. The entropy formula for the Ricci flow and its geometric applications.

March 30 Thu

8:00-9:30 AM

Lecture 5: Singularity Formation in Higher Dimensions

Reference: Bamler, R. H. Recent developments in Ricci flows.

4. 授课地点 Course Link:

Tencent Meeting ID： 86966997109 (password:0323)

Anyone interested in the course is welcome to join. In case of a technical failure or any other emergency, please come back to refresh this webpage for further notices.

腾讯会议：86966997109 (密码0323)

对本次课程感兴趣的老师、同学可自行线上参加。如果出现网络等或其他意外故障，请大家及时访问此网页获得最新信息。

5. 联系人 Contact

杨波 boyang@xmu.edu.cn

叶老师，0592-2580036，tymath2@xmu.edu.cn

6. 课程资源