Shanghai Conference of Analysis and Geometry
Dec. 27-28, 2025
Venue：USTC Shanghai Institute for Advanced Studies 1A-1329
Organizing Parties：
University of Science and Technology of China
ShanghaiTech University
University of Chinese Academy of Sciences
Organizing Committee：
Zhongshan An（University of Science and Technology of China）
Gao Chen（University of Science and Technology of China）
Xiuxiong Chen（University of Science and Technology of China）
Chengjian Yao（ShanghaiTech University）
Haitian Yue（ShanghaiTech University）
Kai Zheng（University of Chinese Academy of Sciences）
Contact：igp@ustc.edu.cn
Speakers：
Yifan Chen（UC Berkeley）
Title：when singular Kahler-Einstein metrics are Kahler currents
Abstract：We show that a general class of singular K\ahler metrics with Ricci curvature bounded below define K\ahler currents. In particular the result applies to singular K\ahler-Einstein metrics on klt pairs. If time permits, we will also talk about some application of this result. This is a joint work with Shih-Kai Chiu, Max Hallgren, Gabor Szekelyhidi, Tat Dat To, and Freid Tong.
Shaoming Guo（Nankai University）
Title：Kakeya problems on manifolds and their classifications
Abstract：The talk is about the Euclidean Kakeya problem and its generalizations on manifolds. We will also talk about classifications of Kakeya problems on manifolds, both in the analytic aspect and in the more geometric aspect.
Yi Li（SIMIS/Fudan University）
Title：Curvature estimates on some geometric flows
Abstract：In this talk, I will give curvature esrimates on some geometric flows, includint Ricci flow and G2 flow, and their applications.
Siran Li（Shanghai Jiao Tong University）
Title：TBA
Abstract：TBA
Jianli Liu（Shanghai University）
Title：Formation of singularities for the relativistic membrane equation with radial symmetry
Abstract：The relativistic membrane equation occupies a particularly significant position as it describes the dynamics of timelike extremal hypersurfaces in the Minkowski spacetime. The relativistic membrane equation with radial symmetry can be rewritten as a first order hyperbolic system. Making use of the characteristic decomposition method, we give the formation of singularities for the relativistic membrane equation. Indeed, the singularity occurs when the hypersurface turns from being timelike to being null. This generalizes the result of Kong, Sun and Zhou’s work for one-dimensional case [J Math Phys 47(1): 013503, 2006]. This work is jointed with Cai Lv of Shanghai University.
Langte Ma（Shanghai Jiao Tong University）
Title：TBA
Abstract：TBA
Jian Wang（University of Chinese Academy of Sciences）
Title：Mass Lower Bounds for asymptotically locally flat 4-manifolds
Abstract：The mass is a fundamental global geometric invariant with deep connections to scalar curvature. In this talk, we will present the mass for asymptotically locally flat (ALF) 4-manifolds and establish the corresponding mass inequality. Specifically, we will talk about how the topology at infinity influences the mass within the ALF setting.
Wei Wang（Zhejiang University）
Title：TBA
Abstract：TBA
Junsheng Zhang（New York University Courant Institute）
Title：TBA
Abstract：TBA
