Gross-Siebert's slab functions and open GW invariants for toric   Calabi-Yau manifolds
  This paper derives an equality between the slab functions in Gross-Siebert program and generating functions of open Gromov-Witten invariants for toric Calabi-Yau manifolds, and thereby confirms a conjecture of Gross-Siebert on symplectic enumerative meaning of slab functions. The proof is based on the open mirror theorem of Chan-Cho-Lau-Tseng \cite{CCLT13}. It shows an instance of correspondence between tropical and symplectic geometry in the open sector. 
Siu-Cheong Lau
math.AG math.SG