N=2 String Geometry and the Heavenly Equations

In this paper we survey some of the relations between Plebański description of self-dual gravity through the heavenly equations and the physics (and mathematics) of N = 2 Strings. In particular we focus on the correspondence between the infinite hierarchy in the ground ring structure of BRST operators and its associated Boyer-Plebański construction of infinite conserved quantities in self-dual gravity. We comment on “Mirror Symmetry” in these models and the large-N duality between topological N = 4 gauge theories in two dimensions and topological gravity in four dimensions. Finally D-branes in this context are briefly outlined.