Gauss Periods

：万大庆（美国加州大学欧文分校）
：2025-10-20 16:30
：海韵园实验楼S102

报告人：万大庆（美国加州大学欧文分校）

时  间：2025年10月20日16:30

地  点：海韵园实验楼S102

内容摘要:

Gauss periods are exponential sums over multiplicative subgroups of finite fields. They were introduced by Gauss (1801) to solve the ancient geometric problem of constructing regular n-gon using a compass and straightedge. Since then, Gauss periods have been studied extensively and have found applications in coding theory, graph theory and combinatorial design. In this expository lecture, we present a global overview of this subject. We view Gauss periods as a multi-set of complex numbers, p-adic numbers and algebraic numbers. We will discuss the many open problems and conjectures arising naturally in the process.

个人简介：

万大庆，美国加州大学欧文分校(University of California, Irvine)教授,主要从事数论与算术代数几何、算法与计算复杂性的研究,涉及有限域上的ζ-函数与L-函数、p进分析、计算数论及编码理论等方面的研究。代表性成果发表于Annals of Mathematics、Inventiones Mathematicae、Journal of the American Mathematical Society 等数学顶尖期刊和FOCS、STOC、FOCM、IEEE IT等计算机领域顶会和顶级期刊,曾获国际华人数学家晨兴数学银奖、教育部海外杰出青年学者、入选中国科学院“百人计划”。

 

联系人：祝辉林