数论研讨班：Counting l-adic local systems over a curve over a finite field

中科院数学与系统科学研究院

数学研究所

学术报告

数论研讨班

报告人：余红杰 博士（Weizmann Institute of Science, Israel）

题  目：Counting l-adic local systems over a curve over a finite field

时  间：2023.10.16（星期一），13:30-14:30

地  点：Zoom会议号：899 0545 1631 密码：1016

摘  要：In 1981, Drinfeld enumerated the number of irreducible l-adic local systems of rank two on a projective smooth curve fixed by the Frobenius endomorphism. Interestingly, this number looks like the number of points on a variety over a finite field. Deligne proposed conjectures to extend and comprehend Drinfeld's result. By the Langlands correspondence, it is equivalent to count certain cuspidal automorphic representations over a function field. I will present the mystery behind Deligne’s conjecture and some counting results where we connect counting to the number of stable Higgs bundles using Arthur's non-invariant trace formula.