数论与代数几何讨论班
报告人：蔡毓麟 (西湖大学 hjc888老品牌黄金城)
报告时间: 2022年10月26日（周三)，10月28日(周五)上午10：30-11:30
腾讯会议号：368-3649-4653 密码: 2022
报告题目:
Integral points on modular curves
(The first and second talks)
报告摘要:
Abstract: The aim of this series of talks is to study the integral points on modular curves using Diophantine approximation. We divide the series into 4 talks.
The first talk: Integral points on algebraic curves.
In this talk, we will introduce the notion of height, the Baker’s inequality and Σ-units. We will give different versions of Chavelley-Weil theorem if we have enough time. Because of the limit of the time, we may not get into every detail of the proofs, but we will focus on their applications.
The second talk: Modular forms and modular curves.
The modular forms and modular curves will be introduced in this talk. This is a rich theory, so we will only focus on the results that are useful for our topics and sketch the proofs. Most of the results can be found in the classical books for modular forms.
The third talk: Modular units.
The modular units are Σ-units of modular curves. We will give a basis of the group of modular units and state some approximation results of Σ-units.
The last talk: Integral points on modular curves.
In this talk, we will apply our results in the last talks to give an explicit bound of heights of integral points on modular curves.
报告人简介:
蔡毓麟，博士毕业于波尔多大学，现为西湖大学博士后，主要从事丢番图方程整点和有理点及其相关理论的研究。已在Communications in Mathematics，J. Number Theory Mosc. J. Comb. Number Theory等著名期刊发表多篇论文。
邀请人：陈伊凡
