中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
华罗庚青年数学论坛报告
Speaker: Tianqi Wang（耶鲁大学）
Inviter: 周正一
Language: Chinese
Title: Ending currents of hyperbolic group representations
Time & Venue: 2026年8月9日（星期日） 9:30-10:30 南楼N820
Abstract: We introduce notions of ending currents for properly discontinuous isometric actions of hyperbolic groups on Gromov hyperbolic spaces, generalizing Thurston’s ending laminations from the setting of Kleinian surface groups. In contrast with the 3-dimensional picture, we construct an example of geometrically finite representations of a closed surface group into SO+(4,1) whose parabolicity appears only at a non-simple closed geodesic, and an example of hyperbolic group extensions where different notions of ending currents, which coincide in the 3-dimensional setting, become distinct. This is joint work with Yair Minsky.
Speaker: 周胜铉（图卢兹大学）
Inviter: 周正一
Language: Chinese
Title: An Explicit Uniform Bound for Rational Points on Curves
Time & Venue: 2026年8月9日（星期日） 11:00-12:00 南楼N820
Abstract: The celebrated Mordell conjecture, proved by Faltings, asserts that a curve of genus greater than one over a number field has only finitely many rational points. A deep uniform upper bound on the number of rational points follows from Vojta's inequality and the recent works of Dimitrov-Gao-Habegger and Kühne. In this talk, I will introduce an explicit version of this uniform bound. Our approach relies on analyzing Arakelov Kähler forms via localization of Bergman kernels. This is joint work with Jiawei Yu and Xinyi Yuan.
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