29/3, IMPA, Auditorio 1.
10:3011:30 
Alex Abreu (UFF),
Mapa de Abel universal.
Resumo. Nesta palestra mostraremos como resolver o mapa de Abel universal M_{g,n}→J_{g}, onde J_{g} é a compactificação de Esteves da Jacobiana universal. Para isso utilizaremos a geometria tropical, em particular resolveremos o problema análogo para o moduli de curvas tropicais.
 12:0013:00 
Dhruv Ranganathan (MIT),
Curves, maps, and singularities in genus one.
Resumo. I will outline a new framework based on tropical and logarithmic methods to study genus one curve singularities and discuss its relationship with the geometry of moduli spaces. I will focus on two applications of these ideas. First, they allow one to explicitly factorize the rational maps among log canonical models of the moduli space of npointed elliptic curves. Second, they reveal a modular interpretation for Vakil and Zinger's famous desingularization of the space of elliptic curves in projective space, as well as a short and conceptual proof of that result. In fact, the same methods yield logarithmically smooth compactifications of the space of elliptic curves in toric varieties. If time permits, I will discuss applications to some questions in classical enumerative geometry. This is based on joint work with Keli SantosParker and Jonathan Wise, building on prior work of Speyer, Smyth, Viscardi, Vakil, and Zinger.

