时间：2021年9月25-26日
地点：杭州花家山庄（西湖区三台山路25号）
1.时间安排：9月25日 09:00-10:20
主讲嘉宾：肖梁（北京大学）
报告题目：Basic height theory
报告摘要：The goal is to introduce Weil's height machine, Neron-Tate height of abelian varieties, and the application to the Mordell-Weil theorem.
2.时间安排：9月25日 10:30-11:50
主讲嘉宾：唐舜（首都师范大学）
报告题目：Basic Arakelov theory
报告摘要：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.时间安排：9月25日 13:30-14:30
主讲嘉宾：张通（华东师范大学）
报告题目：Basics on the moduli spaces of curves
报告摘要：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.时间安排：9月25日 14:40-15:40
主讲嘉宾：袁新意（北京大学）
报告题目：Introduction to the Mordell conjecture
报告摘要：This is an overview of the proofs of the Mordell conjecture, with some details on Vojta's proof (simplified by Faltings, Bombieri).
5.时间安排：9月25日 16:10-17:10
主讲嘉宾：谢俊逸（法国国家科学研究中心）
报告题目：Introduction to Berkovich spaces
报告摘要：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.时间安排：9月25日 17:20-18:20
主讲嘉宾：谢俊逸（法国国家科学研究中心）
报告题目：Introduction to the Bogomolov conjecture
报告摘要：This is an introduction to various forms of the Bogomolov conjecture, with some details on the lower bound of ωa2 for curves in terms of the φ-invariant following Zhang, Cinkir, de Jong.
7.时间安排：9月26日 9:00-11:50
主讲嘉宾：袁新意（北京大学）
报告题目：Uniform Mordell-Lang and uniform Bogomolov I,II
报告摘要：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.
