The Strominger-Yau-Zaslow conjecture expect that the Calabi-Yau manifolds admits special Lagrangian fibrations and the fibration collapse near the large complex structure limit. In this talk, I will explain both phenomena in the case of log Calabi-Yau surfaces. Given a del Pezzo surface Y with a smooth anti-canonical divisor D. I will briefly explain the existence of the special Lagrangian fibration on the complement X=Y\D using Lagrangian mean curvature flow. Then I will focus on the behavior of the Ricci-flat metric as D degenerating to a nodal rational curve. By studying the Ricci-flat metric on the corresponding rational elliptic surfaces, we will see the collapsing of special fibration near infinity.

This is based on the joint work with T. Collins and A. Jacob.