ABSTRACT

Understanding the degeneration of Fano varieties is a central theme in the construction of the moduli space of Fano varieties. In this talk we will describe our trilogy of works to settle the uniqueness of degeneration, with an assumption of K-polystability. Applications include the solution of Donaldson-Sun’s conjecture on the algebraicity of the metric tangent cone, the reductivity of the automorphism of a K-polystable Fano variety, and the existence of a Hausdorff K-moduli. If time permits, I will also discuss a strategy to attack the existence of the degeneration, and what the main difficulty remains there. Different parts are joint works with Jarod Alper, Harold Blum, Daniel Halpern-Leistner, Chi Li, Yuchen Liu and Xiaowei Wang. 

BRIEF BIO

Dr. Chenyang Xu is currently a professor at MIT. He obtained his bachelor and master degrees in mathematics from Peking University in 2002 and 2004 respectively, and completed his Ph.D under the supervision of Professor János Kollár at Princeton University in 2008. He was then a CLE instructor at MIT from 2008 to 2011 and an assistant professor at the University of Utah in 2012. In 2012, he joined the faculty of the Beijing International Center for Mathematical Research of Peking University. During this period, Xu was awarded the Future Science Prize in Mathematics and Computer Science in 2017 and the New Horizons in Mathematics Prize in 2019. In 2020, he became a Fellow of the American Mathematical Society. 

His research interests lie primarily in higher-dimensional algebraic geometry, in particular, the geometric and arithmetic theory of rational connected varieties, the minimal model program(MMP) and classification of varieties, stability of birational geometry, and the topology and geometry of singularities. 

ZOOM INFO (Updated)

ID: 620 7540 7327

Password: 877711

https://zoom.com.cn/j/62075407327?pwd=c3RXL3VlTXRiaG0zVDU4bndSQWM4QT09

For more information about this seminar, please see below.

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【Wednesday Online Seminar on Geometric Analysis】

This is the ninth 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)

June 17, 2020      Ben Andrews (Australian National University)

June 24, 2020      Shiguang Ma(Nankai University)