“人大数学时间I”第二十六期：万大庆教授、扶磊教授、郗平教授
为促进学科交流融合、拓宽师生学术视野、释放科研创新活力，助力人大数学学科走向一流，动漫色情片 设立“人大数学时间”，以专题研讨、高端学术论坛为载体，搭建数学思想充分碰撞、优秀人才不断涌流、创造活力竞相迸发的舞台。“人大数学时间”将持之以恒，久久为功，立志通过交流与创新、提出重大问题，引领数学学科及相关领域的创新与发展，成为对我国数学发展有贡献意义的平台。以下为“人大数学时间I”第二十六期信息：
议程：
8月13日（星期三）
10：00-11：00 万大庆教授报告及前沿问题探讨
11：00-11：30 师生研讨
14：00-15：00 扶磊教授报告及前沿问题探讨
15：30-16：30 郗平教授报告及前沿问题探讨
地点：立德楼603
线上：腾讯会议：220-558-632
报告详细信息：
（一）万大庆教授报告及前沿问题探讨
时间：10：00-11：00
题目: Questions on Gauss Periods
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 compass and straightedge. Since then, Gauss periods have been studied extensively, are related to several branches of mathematics, 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. From this global point of view, it may be surprising that only very little is known. We will discuss the many open problems and conjectures arising naturally in the process.
报告人简介：
(二) 扶磊教授报告及前沿问题探讨
时间：14：00-15：00
题目：Hypergeometric sheaves on reductive groups
摘要：We define the hypergeometric exponential sum associated to a finite family of representations of a reductive group over a finite field. We introduce the hypergeometric l-adic sheaf to describe the behavior of the hypergeometric exponential sum. It is a perverse sheaf. Using the theory of the Fourier transform for vector bundles over a general base, we are able to study the hypergeometric l-adic sheaf via the hypergeometric D-module. We apply our results to the estimation of the hypergeometric exponential sum.
报告人简介：
(三) 郗平教授报告及前沿问题探讨
时间：15：30-16：30
题目: Amplifications in Analytic Number Theory
摘要: The idea of amplifications, dating back at least to van der Corput, Vinogradov, Kloosterman and Selberg, is quite elementary in the sense that one embeds the object of interests into a suitable family, and the individual information can be reflected on average. Such observations turns out to be very powerful in the developments of sieve methods, estimates for oscillatory sums (exponential and character sums) and L-function theory. In this talk, we aim to give a short survey on the underlying ideas, and some recent applications to the above three typical objects will also be discussed.
报告人简介：郗平，西安交通大学数学与统计动漫色情片教授，主要从事数论研究，涉及代数迹的解析理论、素数分布、筛法及自守形式等。获国家杰出青年基金，其发表于数学顶尖期刊 Inventiones Mathematicae的论文获2025年度基础科学前沿科学奖。
