The decomposition formula for log Gromov-Witten invariants

One major goal of log Gromov-Witten theory is to reconstruct usual Gromov-Witten invariants of a smooth projective variety X using appropriate invariants of a degeneration of X. The decomposition formula is the first step toward this. It breaks the invariants of a degeneration of X into terms which can be classified by the dual complexes/tropical curves of stable log maps. This leads to a decomposition on the level of virtual cycles. This is a joint work with Dan Abramovich, Mark Gross, and Bernd Siebert.