29/3, IMPA, Auditorio 1.
Alex Abreu (UFF),
Mapa de Abel universal.|
Resumo. Nesta palestra mostraremos como resolver o mapa de Abel universal Mg,n→Jg, onde Jg 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.
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 n-pointed 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 Santos-Parker and Jonathan Wise, building on prior work of Speyer, Smyth, Viscardi, Vakil, and Zinger.