Hyperelliptic curves, scanning, and moments of quadratic L-functions

In this talk, I will discuss recent results, in joint work with Bergström, Petersen, and Westerland, concerning the relationship between the conjectural asymptotic formula for moments of quadratic Dirichlet L-series in the function field setting, and the stable cohomology of moduli spaces of hyperelliptic curves with coefficients in symplectic representations.