时间：2025年10月24日（周五）14:45-15:45
地点：E4-233
主讲人：Javier Fresán, Sorbonne University
主讲人简介：Professor Fresán graduated from the University of Paris 13 in 2013 and now is a professor at Sorbonne University in Paris. Prior to joining Sorbonne in 2022, he was a Monge Professor at École Polytechnique since 2017. He had worked at ETH Zürich and Max-Planck-Institut für Mathematik Bonn as a postdoctoral researcher between 2013 and 2017.
Professor Fresán is an expert in number theory and algebraic geometry. His research is centered on motives, periods, special functions, and related subjects. He was awarded the CNRS Bronze Medal in 2023 for his remarkable contributions to period theory, and received ICBS Frontiers of Science Awards in 2023 and 2025 with his collaborates.
讲座主题：Equidistribution of exponential sums on algebraic groups
讲座摘要: I will present a joint work with Arthur Forey and Emmanuel Kowalski in which we prove a general theorem about the equidistribution of discrete Fourier transforms of trace functions of perverse sheaves on commutative algebraic groups over finite fields. In order to make this equidistribution result concrete for a given trace function, one needs to compute a tannakian fundamental group associated with the corresponding perverse sheaf, which can in general be challenging. I will show a family of examples in which this can be done using tools from representation theory (Larsen's alternative) and combinatorics (Sidon sets). If time permits, I will also mention a recent application to graph theory obtained in collaboration with Yuval Wigderson.
