ABSTRACT 

We prove that the Weil-Petersson metric extends uniquely to a Kahler current with continuous local potentials on the KSBA compactification of the moduli space of Kahler-Einstein manifolds with negative first Chern class. In particular, the KSBA moduli space has finite volume with respect to the Weil-Petersson metric. Our results are a high dimensional generalization of Wolpert's theorem for the moduli space of compact Riemann surfaces of fixed genus greater than one.

BRIEF BIO

Dr. Jian Song is currently a Professor in the department of Mathematics at Rutgers University. He received his Ph.D from Columbia University in 2004. From 2004 to 2007, he was J.J. Sylvester Assistant Professor at John Hopkins University. His research interests lie in geometric analysis and complex geometry. 

ZOOM INFO

ID: 635 9210 9214

Password: 033354

https://zoom.com.cn/j/63592109214?pwd=SGFRUnRSUzE2eDlmOFVOT2h4UzB2UT09

For more information about this seminar, please see below.

【Wednesday Online Seminar on Geometric Analysis】

This is the 15th 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)