中科院数学与系统科学研究院数学研究所学术报告表示论研讨班

报告人：杨若涛 博士（Skolkovo Institute of Science and Technology, Moscow, Russia）

题  目：An introduction to the Langlands program and the Gaiotto conjecture

时  间：2023.10.16（星期一），14:45-15:45

地  点：Zoom会议号：886 9374 5380 密码：1016

摘  要：A conjecture of Gaiotto constructs a geometrization of the category of representations of quantum supergroups. This geometrization is given by the category of twisted D-modules on the affine Grassmannian with a certain equivariant condition. In this talk, we will begin by reviewing the background of the Gaiotto conjecture, particularly the history of the Langlands program, and then we will give the precise statement and introduce recent progress on the Gaiotto conjecture and related topics.

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.