Dhruv Ranganathan, MIT
The moduli space of stable maps is a fundamental object in modern enumerative geometry. The spaces acquire their most beautiful geometry when considering stable maps from genus 0 curves to projective space. In higher genus, the situation is chaotic: Vakil shows that the space of stable maps have an essentially unconstrained local geometry. I will explain how tropical geometry leads to an understanding of the geometry of the moduli space of maps in genus one and allows us to construct smooth and compact spaces of parametrizing elliptic curves in any toric variety. This leads to a modular interpretation of a well-known desingularization of the space of stable maps to projective space, due to Vakil and Zinger, as well as a number of applications to tropical enumerative geometry.
MC 5403