Notification: we have updated zoom ID and password and rescheduled our meeting to 10:00 - 11:00 a.m on May 6th. 

Sorry about the inconvenience and thank you very much for your patience and understanding.

Abstract:

In this talk I will survey recent work with Kleiner in which we verify two topological conjectures using Ricci flow. First, we classify the homotopy type of every 3-dimensional spherical space form. This proves the Generalized Smale Conjecture and gives an alternative proof of the Smale Conjecture, which was originally due to Hatcher. Second, we show that the space of metrics with positive scalar curvature on every 3-manifold is either contractible or empty. This completes work initiated by Marques.

Our proof is based on a new uniqueness theorem for singular Ricci flows, which I have previously obtained with Kleiner. Singular Ricci flows were inspired by Perelman’s proof of the Poincaré and Geometrization Conjectures, which relied on a flow in which singularities were removed by a certain surgery construction. Since this surgery construction depended on various auxiliary parameters, the resulting flow was not uniquely determined by its initial data. Perelman therefore conjectured that there must be a canonical, weak Ricci flow that automatically "flows through its singularities” at an infinitesimal scale. Our work on the uniqueness of singular Ricci flows gives an affirmative answer to Perelman's conjecture and allows the study of continuous families of singular Ricci flows leading to the topological applications mentioned above.

About the speaker:

Dr. Richard Bamler is currently an associate professor at UC Berkeley. He received his undergraduate education at the University of Munich in Germany, where he was mentored by Professor Bernhard Leeb. In 2011, he received his Ph.D under the supervision of Professor Gang Tian at Princeton. After a postdoc at Stanford University, he joined the faculty of UC Berkeley in 2014. His field of research is geometric analysis. He is particularly interested in Ricci flow. A lot of his work concerns Ricci flow in dimension 3, extending work of Perelman, which led to the resolution of the Poincaré and Geometrization Conjectures.

ZOOM INFO(updated):

Meeting ID: 647 7240 7964
Password: 089645

To join the meeting, you may visit 

https://zoom.com.cn/j/64772407964?pwd=dVg5akxxd2JtQmkwLzI2aVBEaGt5QT09

For more information about this seminar, please see below. 

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【Wednesday Online Seminar on Geometric Analysis】

This is the fifth talk of Wednesday online seminar on geometric analysis, which is an online seminar organized by Prof. Gang Tian, Prof. Jie Qing, Prof. Zhenlei Zhang, and Prof. Xiaohua Zhu. 

The seminar is scheduled 9:30 - 10:30 a.m. (Beijing time) every Wednesday on Zoom. 

Below is a list of invited speakers:

April 8, 2020        Wenshuai Jiang (Zhejiang University)

April 15, 2020      Chi Li (Purdue University)

April 22, 2020      Lu Wang (Caltech)

April 29, 2020      Jianchun Chu (Northwestern University)

May 6, 2020        Richard Bamler (UC Berkeley)

May 13, 2020       Xin Zhou (UC Santa Barbara)

May 20, 2020       Daniel Stern (University of Toronto)

May 27, 2020       Jeff Streets (UC Irvine)

June 3, 2020        Chenyang Xu (MIT)

June 10, 2020      Yi Lai (UC Berkeley)