I'll discuss an ongoing joint project with Lopez, Pflueger, and Teixidor, in which we use a surprising theorem on random standard Young tableaux to give a new proof, using degenerations and limit-linear series, of the classical formula of Eisenbud-Harris and Pirola for the genus of the Brill-Noether curve. No background will be assumed.
Topology of tropical moduli spaces
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}. I will report on 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.
