ABSTRACT

We present a new compactness theory of Ricci flows. This theory states that any sequence of Ricci flows that is pointed in an appropriate sense, subsequentially converges to a synthetic flow. Under a natural non-collapsing condition, this limiting flow is smooth on the complement of a singular set of parabolic codimension at least 4. We furthermore obtain a stratification of the singular set with optimal dimensional bounds depending on the symmetries of the tangent flows. Our methods also imply the corresponding quantitative stratification result and  the expected $L^p$-curvature bounds. As an application we obtain a description of the singularity formation at the first singular time and a long-time characterization of immortal flows, which generalizes the thick-thin decomposition in dimension 3. We also obtain a backwards pseudolocality theorem and discuss several other applications.

ZOOM INFO

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https://zoom.com.cn/j/64686685589?pwd=b05sVVluNmI2RzZ2RkRqV1lib0RmZz09

BRIEF BIO

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.

For more information about this seminar, please see below.

【Wednesday Online Seminar on Geometric Analysis】

This is the 17th 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.

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)

June 17, 2020       Ben Andrews (Australian National University)

June 24, 2020       Shiguang Ma (Nankai University) 

July 1, 2020           Yuchen Liu (Yale University)

July 7, 2020           Min-Chun Hong (The University of Queensland)

July 15, 2020         Jian Song (Rutgers University)

September 8          Martin Kerin (NUI Galway)

September 23       Richard Bamler (UC Berkeley)