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.

Brief biography: Shengxuan Zhou is currently a CIMI postdoc in Institut de Mathématiques de Toulouse. He obtained his PhD in July 2024 at Peking University under the supervision of Prof. Gang Tian. His research interest lies in Kähler Geometry, Riemannian Geometry and related topics.

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