Time：Sep 25-26, 2021
Venue：HANGZHOU HUA JIA SHAN RESORT
1.Time：09:00-10:20, Sep 25th
Speaker：Liang Xiao, Peking University
Title：Basic height theory
Abstract：The goal is to introduce Weil's height machine, Neron-Tate height of abelian varieties, and the application to the Mordell-Weil theorem.
2.Time：10:30-11:50, Sep 25th
Speaker：Shun Tang, Capital Normal University
Title：Basic Arakelov theory
Abstract：This lecture introduces arithmetic divisors and hermitian line bundles over arithmetic varieties, and defines their top intersection numbers. Define height functions associated to hermitian line bundles. Introduce ampleness, bigness, nefness of hermitian line bundles.
3.Time：13:30-14:30, Sep 25th
Speaker：Tong Zhang, East China Normal University
Title：Basics on the moduli spaces of curves
Abstract：This is a review of the definition and GIT construction of the moduli spaces of smooth curves and stable curves. Introduce the tautological divisors (Hodge bundle, boundary divisors) over the moduli space of stable curves. Introduce Noether's formula.
4.Time：14:40-15:40, Sep 25th
Speaker：Xinyi Yuan, Peking University
Title：Introduction to the Mordell conjecture
Abstract：This is an overview of the proofs of the Mordell conjecture, with some details on Vojta's proof (simplified by Faltings, Bombieri).
5.Time：16:10-17:10, Sep 25th
Speaker：Junyi Xie, Centre national de la recherche scientifique
Title：Introduction to Berkovich spaces
Abstract：This is an outline of the theory of Berkovich analytic spaces. It will also cover metrized line bundles, and Green's functions over Berkovich spaces.
6.Time：17:20-18:20, Sep 25th
Speaker：Junyi Xie, Centre national de la recherche scientifique
Title：Introduction to the Bogomolov conjecture
Abstract：This is an introduction to various forms of the Bogomolov conjecture, with some details on the lower bound ofωa2for curves in terms of the φ-invariant following Zhang, Cinkir, de Jong.
7.Time：9:00-11:50, Sep 26th
Speaker：Xinyi Yuan, Peking University
Title：Uniform Mordell-Lang and uniform Bogomolov I,II
Abstract：This is an introduction to the recent results on the uniform Mordell-Lang problem and the uniform Bogomolov problem of Dimitrov-Habegger-Gao, Kühne and Yuan. We will focus on Yuan's approach.
