Title:  Special Lagrangian tori and mirror symmetry.

Abstract:  This talk will focus on a geometric proposal for constructing
the mirror of a compact Kahler manifold equipped with an anticanonical
divisor, extending the Strominger-Yau-Zaslow conjecture beyond the
Calabi-Yau case. The mirror manifold is constructed as a (complexified)
moduli space of special Lagrangian tori, and the Landau-Ginzburg
superpotential is defined by a weighted count of holomorphic discs.
We will give examples, both in the toric and in the non-toric setting, to
illustrate the construction and the manner in which "instanton corrections"
arise from exceptional discs and wall-crossing phenomena.