时间：2025年4月25日（周五）10:00-11:00
地点：E4-233
主持人：Zhuchao Ji, ITS
主讲人：Songyan Xie, AMSS, CAS
主讲人简介：Dr. Song-Yan Xie obtained his Ph.D. in Mathematics from Paris-Sud University in 2016. He is currently a Professor at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences (CAS), where he has been a faculty member since 2018. His research centers on several complex variables and complex geometry, with a particular emphasis on the interplay between complex analytic methods and geometric structures. Dr. Xie has made notable contributions to the study of the ampleness of cotangent bundles, the theory of Nevanlinna currents, and the construction of universal holomorphic maps with slow growth. His work has been published in prominent journals, including Inventiones Mathematicae, Journal de Mathématiques Pures et Appliquées, and Mathematische Annalen.
讲座主题：Hole Probability of Random Zeros on Compact Riemann Surfaces
讲座摘要: This presentation explores the intriguing phenomenon of hole probability—the probability that certain regions on a compact Riemann surface are devoid of zeros of random holomorphic sections. A particularly compelling aspect of this study is the so-called "hole phenomenon", which reveals unexpected patterns in the spatial distribution of these zeros. We discuss recent progress in understanding this phenomenon, utilising tools from complex analysis and algebraic geometry, including Zelditch's density formula, Abel-Jacobi theory, and Fekete point theory. Additionally, we introduce a novel perturbation method that significantly advances our analytical capabilities. This work is the result of a collaboration with Hao Wu from Nanjing University (arXiv:2406.19114).
