# 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.

Speaker:

Denis Auroux

MIT

Event Location:

Fine Hall 314