邓太旺 , 谢尔盖·奥布莱津 , 佘东明

余红杰

2026年10月15日 13:30 至 14:30

A3-4-301

Zoom 435 529 7909 (BIMSA)

In 1981, Drinfeld counted the irreducible rank-two ℓ-adic local systems on a smooth projective curve over a finite field that are fixed by the Frobenius endomorphism. Strikingly, the resulting number has the shape of a point count on a variety over a finite field, pointing to a hidden geometric structure. Deligne later proposed conjectures aimed at extending and conceptualizing Drinfeld’s enumeration. Through the Langlands correspondence for function fields, this enumeration is equivalent to counting certain cuspidal automorphic representations. Ngô Bảo Châu observed that trace formulas over a Lie algebra compute point counts on the moduli space of Higgs bundles over a curve over a finite field. Using this observation, we connect such enumerative problems to counts of stable Higgs bundles via Arthur’s non-invariant trace formula, thereby confirming some of Deligne’s conjectures.