数学研究所

数学科学全国重点实验室

学术报告

多复变与复几何研讨班

SCV&CG Seminar

Speaker: 谢松晏 研究员（中国科学院数学与系统科学研究院）

Inviter: 周向宇 院士

Language: Chinese

Title: Hole Probabilities of Random Zeros on Compact Riemann Surfaces

Time & Venue: 2025年5月22日（星期四） 9:30 - 11:30 & 南楼N913

Abstract: This presentation explores the intriguing phenomenon of hole probabilities—the probabilities 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 "forbidden region 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).