Time：14:00-16:00, Thursday, October 24 2024
Venue：E4-233
Speaker：Hongjie Yu, Morningside Center of Mathematics, Chinese Academy of Sciences
Title：Counting l-adic local systems over a curve
Abstract：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 some counting results where we connect counting to the number of stable Higgs bundles using Arthur's non-invariant trace formula.
