Organizing Committee:

Liu Ruochuan, Tian Gang, Xiao Liang, Xie Junyi, Zhang Jiping

Presentation Session

Host: Liu Ruochuan, Peking University

1:50 - Guest group photo (location: the conference stage)

2:00–2:05 PM – Representative of Peking University: Tian Gang, Peking University

2:05–2:10 PM – Representative of the Future Science Prize: Zhou Kui, Partner of HSG

2:10–2:40 PM – Speaker 1: Xie Junyi, Peking University

Title: Faltings' Theorems via Yuan's Equidistribution Theorem

Abstract: With Ziquan Yang, we give a new proof of Faltings' isogeny theorem via Yuan's equidistribution theorem. This method also gives a new proof of the Mordell conjecture. More precisely, we show that Yuan's equidistribution theorem can be used to “pump” homomorphisms and semisimplicity from finite fields to number fields, thereby reducing Faltings' isogeny theorem directly to Tate's theorem over finite fields. The above proof of Faltings' isogeny theorem, combined with an ultraproduct variant of our method, gives another proof of the Shafarevich conjecture and, via Parshin's trick, a new route to the Mordell conjecture.

2:40–3:10 PM – Speaker 2: Liu Yifeng, Zhejiang University

Title: Gross–Zagier formula for Hilbert modular forms

Abstract: Gross–Zagier formula, discovered 40 years ago, is one of the major cornerstones in the study of the Birch and Swinnerton-Dyer (BSD) conjecture, which is a formula computing central derivatives of L-functions of modular forms of weight 2. It was later generalized by Xinyi Yuan, Shouwu Zhang, and Wei Zhang to Hilbert modular forms of parallel weight 2. In this talk, I will review the history and explain how one can further extend this formula to Hilbert modular forms of general weights.

3:15–3:45 PM – Speaker 3: Zhou Shengxuan, University of Bonn, Germany

Title: A Geometric Viewpoint on Quantitative Uniform Mordell

Abstract: In their recent proof of the quantitative uniform Mordell conjecture, Yu–Yuan–Zhou applied severel ideas and tools from differential geometry to study the Arakelov measure on Riemann surfaces. In this talk, we explain where these geometric viewpoints come from and the intuition behind them.

3:45–4:15 PM – Speaker 4: Yuan Xinyi, Peking University

Title: Arithmetic Bigness and Diophantine Equations

Abstract: In classical Diophantine approximation, one often needs to construct an auxiliary polynomial to control algebraic solutions. In modern terminology, auxiliary polynomials become sections of line bundles, where bigness of line bundles provides a theoretical mechanism to find appropriate sections. With these sections, we can bound heights of rational points, and thus prove important results in Diophantine geometry. In this talk, I will introduce this mechanism in classical terms and in modern terminology, and then talk about my recent works in this framework.

4:15–4:20 - Group photo of all attendees

Panel Discussion Session (4:20–5:00 PM)

Host: Xiao Liang, Peking University

Panelists:

Ding Jian, Peking University

Liu Yi, Peking University

Liu Yifeng, Zhejiang University

Xie Junyi, Peking University

Yuan Xinyi, Peking University