Dan Petersen: Cohomology of local systems on the moduli of principally polarized abelian surfaces

Let A_2 be the moduli space of principally polarized abelian surfaces. To any irreducible representation of Sp(4) one may attach a local system on A_2. I will report on work in which I determined the l-adic cohomology of these local systems in arbitrary degree. This has applications to the study of vector-valued Siegel modular forms and to moduli of curves.