Counting rational curves of arbitrary shape in projective spaces
  We present an approach to a large class of enumerative problems concerning rational curves in projective spaces. This approach uses analysis to obtain topological information about moduli spaces of stable maps. We demonstrate it by enumerating one-component rational curves with a triple point or a tacnodal point in the three-dimensional projective space and with a cusp in any projective space. 
Aleksey Zinger