主讲人：Prof. Edixhoven

Edixhoven 是很有影响的算术代数几何专家, 是对费尔马大定理的解决有贡献的少数几个人之一, 目前为 Compositio 的两主编之一, 以及多个杂志的编委。

时间地点：

11月29日（星期二）15:05--17:00, 清华数学系A112教室

11月30日（星期三）15:05--17:00, 清华数学系A112教室

12月 1日（星期四）15:05--17:00，清华数学系A112教室

12月 6日（星期二）15:00--17:00, 首师大数学院312教室

12月 7日（星期三）15:10--17:00, 首师大数学院311教室

12月 9日（星期五）15:00--17:00, 首师大数学院210教室

备注：

讲座摘要: In the series of 6 lectures I will try to cover the contents of the book that I recently published with Couveignes, Bosman, de Jong and Merkl: Computational aspects of modular forms and Galois representations, Annals of Mathematics Studies, 176, Princeton University Press. Subsequent work of Peter Bruin (PhD thesis 2010) will also be discussed.

In my lectures I will focus on the parts that I know best: modular forms, Galois representations, the application of Arakelov theory in order to bound heights, and how to get exact results from approximations. Concerning the algorithms for approximations, due to Couveignes, who will visit Beijing in April 2012, I will indicate the main ideas.

Lecture 1: Main results and their context. Background on modular curves, modular forms and

Galois representations

Lecture 2: First description of the algorithms. Approximation methods, Bosman's real

computations

Lecture 3: Precise setup of the algorithms. Background on heights and Arakelov theory

Lecture 4: Application of Arakelov theory. Merkl's bounds for Green functions

Lecture5: Bounds for Arakelov invariants. Computing residual Galois representations

Lecture 6: Computation of coefficients of modular forms. Bruin's subsequent work. Application

to theta series