ABSTRACT

K-stability of Fano varieties, introduced by Tian, is an algebro-geometric theory which detects the existence of K\"ahler-Einstein metrics. Recently, the question of whether one can construct nicely behaved moduli spaces for Fano varieties using K-stability has attracted significant interest. More precisely, the Fano K-moduli Conjecture predicts that K-polystable Fano varieties with fixed volume and dimension form a projective good moduli space. In this talk, I will explain the proof of openness of K-semistability for Fano varieties which is one major step in the Fano K-moduli Conjecture. Our proof is a combination of valuative criterion for K-semistability due to Fujita and Li, boundedness of complements due to Birkar, and approximation techniques. This talk is based on joint work with Harold Blum and Chenyang Xu.

BRIEF BIO

Dr. Yuchen Liu is currently a Gibbs Assistant Professor in the math department at Yale University. He received his Ph.D. from Princeton University under the supervision of Professor János Kollár in 2017. For the academic year 2020--2021, Liu will be a Visiting Assistant Professor at Princeton University. Starting from Fall 2021, he will be a Tenure-Track Assistant Professor at Northwestern University. His research interests lie in algebraic geometry, particularly, Fano varieties, K-stability, normalized volumes, moduli spaces, and Brody hyperbolicity.

ZOOM INFO

ID: 653 9152 0354

Password: 626060

https://zoom.com.cn/j/65391520354?pwd=OGpkQng5TUQ4aWJPTWlGbG5teGVpdz09

For more information about this seminar, please see below.

【Wednesday Online Seminar on Geometric Analysis】

This is the 13th 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)