ABSTRACT

In recent work with Mikhail Karpukhin, we relate the problem of maximizing Laplacian eigenvalues over unit-area conformal metrics on a closed surface to certain natural min-max constructions of harmonic maps to high-dimensional spheres. I'll describe our results and several applications to shape optimization problems in spectral geometry, including sharp upper bounds for the first two Steklov eigenvalues on surfaces with fixed genus and any number of boundary components.

BRIEF BIO

Dr. Daniel Stern is currently a postdoctoral fellow at the University of Toronto. He completed his Ph.D in mathematics in 2019 at Princeton University, under the supervision of Professor Fernando Coda Marques. His research addresses geometric and analytic problems arising in the study of harmonic maps, minimal submanifolds, and other geometric PDEs.

ZOOM INFO

Meeting ID：662 5171 4644

Password：202005

To join the meeting, you may visit

https://zoom.com.cn/j/66251714644?pwd=R0doaklycUk4MFpueDNWcHZrZkI2dz09

For more information about this seminar, please see below.

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【Wednesday Online Seminar on Geometric Analysis】

This is the seventh 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)