A conjecture relating instanton calculus in four dimensional supersymmetric
theories and the deformation theory of Lagrangian submanifolds in C-2r inv
ariant under a (subgroup of) Sp(2r, Z) is formulated. This is a four dimens
ional counterpart of the mirror symmetry of topological strings (relating G
romov-Witten invariants and generalized variations of Hedge structure).