I will discuss recent work calculating the top weight cohomology of the moduli space A_g of principally polarized abelian varieties of dimension g for small values of g. The key idea is that this piece of cohomology is encoded combinatorially via the relationship between the boundary complex of a compactification of A_g and the moduli space of tropical abelian varieties.

This is joint work with Madeline Brandt, Melody Chan, Margarida Melo, Gwyneth Moreland, and Corey Wolfe.