motivated by the study of mirror symmetry, strominger-yau-zaslow (syz) conjectured that calabi-yau manifolds admit certain minimal lagrangian fibrations. these minimal lagrangians are the special lagrangian submanifolds studied earlier by harvey-lawson. many of the implication of the syz conjecture is proved and it has been the guiding principle for studying mirror symmetry for a long time. however, not many special lagrangians are known in the literature. in this talk, i will prove the existence of special lagrangian fibration on the complement of a smooth anti-canonical divisor in a (weak) del pezzo surface. if the time allows, i will explain its impact to mirror symmetry. this is joint work with tristan collins and adam jacob.