“Mini-course on topological adelic curves” 招生简章
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：Antoine Sédillot（德国雷根斯堡大学）
：2026-04-25 ——2026-04-30
：海韵园实验楼S205
国家天元数学东南中心拟于2026年4月25日至4月30日开设“Mini-course on topological adelic curves”短课程，相关安排如下：
一、短课程介绍
1. 主讲人：
Antoine Sédillot，德国雷根斯堡大学的博士后研究员。他博士毕业于巴黎西岱大学，师从陈华一教授。他的研究领域为Arakelov理论，主要关注丢番图几何、以及复解析几何与非阿基米德解析几何（Berkovich空间）中的问题。他的主要目标之一是研究丢番图逼近与涅万林纳理论之间的类比。
其代表性成果与预印本包括：
· (With T. Bellitto and A. Pêcher) On the density of sets of the Euclidean plane avoiding distance 1, Discrete Mathematics & Theoretical Computer Science, vol. 23 no. 1, Combinatorics (August 31, 2021)
· Topological adelic curves: Zariski-Riemann spaces, algebraic coverings, Harder-Narsimhan filtrations and heights.
· Pseudo-absolute values: foundations (to appear in Isr. J. Math.).
· Differentiability of the relative chi-volume over an adelic curve (submitted).
· Study of projective varieties over adelic curves, PhD thesis.
2. 课程简介：
In this series of lectures, we will deal with several frameworks used to study the arithmetic of fields of global nature. Starting with the classical Diophantine geometry of function fields and global fields, we will move on to the formalism of adelic curves, recently introduced by Chen and Moriwaki [CM19]. Roughly speaking, a proper adelic curve is the data of a field together with a family of absolutes values parametrised by a measure space satisfying a product formula. Adelic curves are very flexible objects that appear in a wide range of situations and a lot of the usual tools and notions of classical Arakelov geometry have a counterpart on them [CM21, CM24].
The goal of this mini-course is to introduce a variation of the formalism of adelic curves, where we replace the measure parameter space by a topological space. Our principal motivation is the analogy between Diophantine approximation and valuation theory [Voj87]. The price to pay is that we need to enlarge the set of absolute values on a field, yielding the notion of pseudo-absolute values [Séd25a]. Although their definition is elementary, they carry some meaningful geometric information and the space of pseudo-absolute values on a field behaves as an "analytic Zariski-Riemann space".
Once the local theory is settled, we will devote the remaining lectures introducing topolog- ical adelic curves [Séd25b]. This consists in three parts. In the first one, we will define them and give basic constructions and examples. In the second one, we will study the notion of adelic vector bundles, which encodes the intrinsic geometry of the topological adelic curve. Finally, we will give the construction of height functions.
We will try to be as self-contained as possible but nonetheless assume some familiarity with algebraic geometry.
二、课程日期安排
2026年4月25日报到，4月26日-29日上课，4月30日离会。
授课日期 | 授课时间 | 教学内容纲要 |
4月26日 | 09:00-11:00 | Lecture 1: Background and Motivation |
4月27日 | 10:00-12:00 | Lecture 2: Local Theory – Pseudo-Absolute Values |
4月28日 | 15:00-17:00 | Lecture 3: Topological Adelic Curves – Definitions and Basic Constructions |
4月29日 | 09:00-11:00 | Lecture 4: Adelic Vector Bundles and Heights |
三、短课程地点
1. 上课地点：厦门大学海韵园实验楼S205
2. 住宿地点：鹭江佲家酒店，福建省厦门市思明区曾厝垵龙虎山路382号，0592-2199099（国家天元数学东南中心为厦门市外学员提供住宿，标间，两人一间）
3. 用餐地点：海韵食堂
四、招生对象
博士生、硕士生、高年级本科生（招生人数20人）
五、联系人
刘老师（tymath1@xmu.edu.cn）
六、报名
1. 网上报名，请扫描简章下方的二维码登录报名（需上传签字盖章后的附件申请表）。
2. 报名截止日期为2026年4月13日，录取结果将通过邮件的方式通知学员。
3. 学员在厦期间，需遵守相关规定与考勤制度，防范各类风险，严禁下海游泳。
