摘要：

In 1801, Gauss developed his theory of cyclotomic periods to solve the geometric problem of constructing regular n-gon using compass and straightedge. Gauss periods are classical in number theory with important applications in coding theory, graph theory and combinatorial design. The main questions are to determine the number of distinct Gauss periods, their multiplicities and algebraic degrees as algebraic integers. In this lecture, we shalk give an overview of this subject, including a discussion of  several intriguing conjectures.

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几何领域的研究，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向。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，曾获得晨兴数学银奖、教育部海外杰出青年学者、入选中国科学院“百人计划”。

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