Tropical curves, graph complexes, and the cohomology of M_g



Joint with Søren Galatius and Sam Payne. The cohomology ring H^*(M_g,Q)

of the moduli space of curves of genus g is not fully understood, even

for g small. For example, in the 1980s Harer-Zagier showed that the

Euler characteristic (up to sign) grows super-exponentially with g

---yet most of this cohomology is not explicitly known. I will explain

how we obtained new results on the rational cohomology of moduli

spaces of curves of genus g, via Kontsevich's graph complexes and the

moduli space of tropical curves.