关于举行冯宇（天津科技大学）学术报告会的通知

  报告主题: Zariski-dense monodromy of singular hyperbolic metrics on non-hyperbolic Riemann surfaces

  报 告 人:冯宇

  报告时间：2026 年 9 月 30 日（星期三）上午 10:00-11:00

  报告地点： 腾讯会议 491379051

  邀 请 人: 陈麒羽、钟友良 副教授

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数学学院

2026 年 9 月 29 日

报告摘要：

  We prove that the monodromy group of every singular hyperbolic metric on a non-hyperbolic Riemann surface, in the sense of potential theory, is Zariski dense in $\PSL(2,\R)$, confirming a conjecture of the authors. The main new step is to show that a singular hyperbolic metric on an arbitrary parabolic Riemann surface cannot have monodromy contained in a conjugate of the real affine subgroup of $\PSL(2,\R)$. The same argument also gives a direct proof in the compact case. Combined with the nonexistence results for the remaining proper subgroup types, this proves the conjecture. This is joint work with Yiqian Shi, Jijian Song and Bin Xu.

报告人介绍：

  冯宇，博士毕业于中国科学技术大学数学科学学院，现为天津科技大学理学院讲师。主要研究黎曼面上的奇性度量和 Higgs 丛及相关问题，研究成果发表于 The Journal of Geometric Analysis, Communications in Analysis and Geometry,Journal of Geometry and Physics, Annals of Global Analysis and Geometry 等期刊。