Mathematics Colloquium

Based on a number of motivations from differential geometry and mirror symmetry, Strominger-Yau-Zaslow proposed in the 90s that for Calabi-Yau manifolds near the large complex structure limit, there is a special Lagrangian torus fibration. I will try to survey the history on the metric aspect of this conjecture, outline what is expected in complex 3D and beyond, what has been proved, and what we still do not know. Time permitting, I will give a little more details on the example of Fermat family.