Collapsing of abelian fibred Calabi-Yaus and hyperkahler mirror symmetry

We will address the problem of understanding the collapsing of Ricci-flat Kahler metric on abelian fibred projective Calabi-Yau manifolds. We will then explain an application of these results to the Strominger-Yau-Zaslow picture of mirror symmetry for some hyperkahler manifolds. Joint work with Mark Gross and Yuguang Zhang.