Equidistribution of exponential sums over finite fields
Many exponential sums over finite fields, such as Gauss or Salié-Kloosterman sums, appears as the Fourier-Melin transform of the trace function of an l-adic sheaf on a commutative algebraic group. We are interested in the equidistribution of such sums as the character varies. Generalizing work by Katz for the multiplicative group, a Tannakian formalism controls the equidistribution in many cases. This is a work in progress in collaboration with Javier Fresán and Emmanuel Kowalski.
(30 minutes general talk followed by 45 minutes research talk)