Date:
Mon, 07/11/202214:30-16:00
Location:
Ross 70
Title: l-adic local systems, automorphic representations and Higgs bundles
Abstract: In 1981, Drinfeld counted the number of irreducible l-adic local systems of rank two on a projective, smooth and geometrically connected curve over a finite field. Curiously, this number looks like the number of points of a variety over the finite field. Deligne proposed conjectures to extend and understand Drinfeld's result. In this talk, I will present his conjectures and explain the parallel problems in the theory of automorphic forms. Finally, I will present some counting results that involve Higgs bundles on the curve.
Abstract: In 1981, Drinfeld counted the number of irreducible l-adic local systems of rank two on a projective, smooth and geometrically connected curve over a finite field. Curiously, this number looks like the number of points of a variety over the finite field. Deligne proposed conjectures to extend and understand Drinfeld's result. In this talk, I will present his conjectures and explain the parallel problems in the theory of automorphic forms. Finally, I will present some counting results that involve Higgs bundles on the curve.