YMSC seminar on complex algebraic geometry | Counting l-adic local systems on a curve over a finite field

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. In this talk,I will present some counting results where we connect counting to the number of stable Higgs bundles using Arthur's non-invariant trace formula.

Speaker

I am currently an associate professor at the Morningside Center of Mathematics, Chinese Academy of Sciences.

I am doing research on Number theory, representation theory and arithmetic geometry. I am particularly interested in the mathematical objects studied in the Langlands program.