Metric SYZ conjecture

Yang Li, Massachusetts Institute of Technology
Fine Hall 110

The Strominger-Yau-Zaslow conjecture asks to find a special Lagrangian torus fibration on a Calabi-Yau manifold sufficiently close to the large complex structure limit. The conjecture sits at the crossroad of algebraic, symplectic, Riemannian geometry, and mirror symmetry. We will focus on the metric aspects, and primarily on the case of the Fermat family, where one can show the existence of the SYZ fibration in the generic region, namely an open subset of the manifold containing most of the measure.