Algebraic Geometry Seminar

The moduli space of n-marked, genus g tropical curves is a cell complex
that was identified in work of Abramovich-Caporaso-Payne with the boundary
complex of the complex moduli space M_{g,n}. It also has connections to
many other important geometric objects: for example, if g=0, it is the
Billera-Holmes-Vogtmann space of phylogenetic trees, while if n=0, it is a
compactified quotient of Culler-Vogtmann Outer space. In this talk, I will
give new results on the topology of tropical M_{1,n} and M_{2,n},
obtaining as corollaries new calculations of the top-weight cohomology of
the complex moduli spaces M_{1,n} and M_{2,n}. Joint work, in part, with
Galatius and Payne.