ABSTRACT

In classical spectral theory, Equidistribution and Scarring, which are two significant but opposite phenomena, concern the distribution of normalized energy measures for Laplacian eigenfunctions on closed manifolds. The Quantum Ergodicity asserts that in negative curvature almost all subsequence of Laplacian eigenfunctions have their normalized energy measures equidistributing, while Scarring means that some particular subsequence of normalized energy measures concentrate on proper subsets. In this talk, we will present a scarring phenomenon for minimal hypersurfaces for a generic set of smooth metrics. This is a joint work with Antoine Song.

BRIEF BIO

Dr. Xin Zhou is currently an assistant professor at UC Santa Barbara. His research focuses on geometric analysis, with an emphasis on variational theory in geometry. He received his bachelor degree from Tsinghua Unviersity in 2006 and master degree from Peking University in 2008 mentored by Professor Gang Tian. He obtained his Ph.D. from Stanford University in 2013 under the supervision of Professor Richard Schoen. He was a Moore Instructor at MIT from 2013 to 2016.

ZOOM INFO

Meeting ID: 698 6219 1314

Password: 202005

To join the meeting, you may visit

https://zoom.com.cn/j/69862191314?pwd=V3FhREZwVkMxcVoxV3hmQUdNSWdkUT09

For more information about this seminar, please see below. 

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【Wednesday Online Seminar on Geometric Analysis】

This is the sixth 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)