Special Lagrangian fibrations, instanton corrections and mirror symmetry

Friday, March 14, 2008 -
2:00pm to 4:00pm
We study the extension of mirror symmetry to the case of Kahler manifolds which are not Calabi-Yau: the mirror is then a Landau-Ginzburg model, i.e. a noncompact manifold equipped with a holomorphic function called superpotential. The Strominger-Yau-Zaslow conjecture can be extended to this setting by considering special Lagrangian torus fibrations in the complement of an anticanonical divisor, and constructing the superpotential as a weighted count of holomorphic discs. In particular we show how "instanton corrections" arise in this setting from wall-crossing discontinuities in the holomorphic disc counts. Various explicit examples in complex dimension 2 will be considered.
Denis Auroux
Event Location: 
Fine Hall 314