报告摘要：Applications of Fourier analysis to number theory create exponential sums, which are basically of analytic or algebraic types. Estimates for such exponential sums turn out to be very crucial in many applications. In this talk, we aim to give a survey on the study of algebraic exponential sums from different aspects, including complete sums and incomplete sums, one variable cases and high dimensional generalizations, analytic methods and geometric approaches, arithmetic properties and analytic behaviours, individual sums and on average. With some typical examples on hand, we would like to show how algebraic exponential sums are applied in analytic number theory, and also describe how the latter one is used to characterize the former ones.

嘉宾简介：郗平，数学与统计学院教授、博士生导师。主要从事数论方面的研究，涉及代数迹函数的解析理论、素数分布、筛法及自守形式等。相关成果发表于Inventiones mathematicae、Compositio Mathematica、Algebra & Number Theory、IMRN等国际期刊。2020年获得国家杰出青年科学基金资助。