Important problems in special Lagrangian geometry


Dominic Joyce

10:00:00 - 11:00:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Calabi-Yau manifolds are important in String Theory in theoretical physics,and are the subject of the mysterious Mirror Symmetry conjectures. Special Lagrangians also appear in String Theory as \"D-branes\". This led to the SYZ Conjecture, a geometrical explanation of Mirror Symmetry in terms of dual special Lagrangian fibrations of the mirror Calabi-Yau 3-folds, including singular fibres. We discuss progress on understanding singularities of specialLagrangian fibrations, and some other important problems in special Lagrangian geometry, including the Thomas-Yau conjecture, the Schoen-Wolfson programme, and defining invariants counting special Lagrangians.