USTC complex geometry seminar
This is the homepage of a complex geometry seminar organized by Mingchen Xia at USTC, Hefei. If you wish to visit USTC and give a talk, please contact Mingchen.
Forthcoming talks
Speaker: Jiyuan Han, Westlake University
Title: On the existence of weighted-cscK metrics
Time: Oct. 10, 2025 (Friday) 10:00-11:00
Abstract: Weight-cscK metrics provide a universal framework for the study of canonical metrics, e.g, extremal metrics, Kahler Ricci soliton metrics, \mu-cscK metrics. In joint works with Yaxiong Liu, we prove that on a Kahler manifold X, the G-coercivity of weighted Mabuchi functional implies the existence of weighted-cscK metrics. In particular, there exists a weighted-cscK metric if X is a projective manifold that is weighted K-stable for models. We will also discuss some progress on singular varieties.
Speaker: Yan He, Norwegian University of Science and Technology(NTNU)
Title: TBA
Time: Oct. 16, 2025 (Thursday)
Abstract: TBA
Speaker: Yi Yao, Hunan University
Title: Maximal destabilizers for Chow and K-stability
Time: Oct. 30, 2025 (Thursday)
Abstract: When Kahler manifold (X, L) admits cscK metrics, Donaldson uses the balanced metrics to quantize the cscK metrics. In the opposite case, if (X, L) is K-unstable, then the Kodaira embedding of X via kL would be Chow-unstable when k is large enough. In this case, we have a maximal K-destabilizer due to Xia and Li, and a sequence of maximal Chow-destabilizers due to Kempf. A natural question is whether the latter will converge to the former in a certain sense. We propose a variational approach based on Boucksom-Jonsson’s non-Archimedean pluripotential theory. We shall start with the toric setting, where things become very concrete.
Past talks
Speaker: Zhiwei Wang, Beijing Normal University
Title: Recent progress on the SOS conjecture
Time: Sep. 19, 2025 (Friday) 10:00~11:00
Abstract: In this talk, we will introduce our recent progress on the study of the SOS conjecture (proposed by Ebenfelt), which is closely related to the Huang-Ji-Yin gap conjecture in the study of rational proper maps between the complex unit balls. This is based on joint work with Chenlong Yue and Professor Xiangyu Zhou.
Speaker: Zhangchi Chen, East China Normal University
Title: Around the unique ergodicity of holomorphic foliations
Time: Sep. 11, 2025 (Thursday) 10:00~11:00
Abstract: Holomorphic foliations are geometric structures to foliate high dimensional complex manifolds with low dimensional ones (called leaves). The key problem in this area is to study the density and the distribution of leaves. Fornaess-Dinh-Nguyen-Sibony proved that in compact Kahler surfaces, foliations with only hyperbolic singularities admits unique ergodicity. In particular, if the foliation does not direct any positive closed currents, then there is a unique (up to scaling) positive harmonic current directed by it. As a consequence, each leaf is dense and has the same distribution in the sense of Nevanlinna currents. In this talk I will introduce the basic concepts about holomorphic foliations, hyperbolic singularities, harmonic currents. I will review the unique ergodicity, and talk about my result on the Lelong number of directed harmonic currents. Finally, I will talk about some open problems.
