Fluxes are important in string theory because they provide a mechanism for stabilization of vacua which is crucial for phenomenological applications. On the mathematical side fluxes pose the question of the natural extension of many of the structures in string theory. For example, the formulation of mirror symmetry in the presence of fluxes is not known. In this lectures we review the interplay between supersymmetry, nonlinear sigma models and target space geometry. We attempt to use these physicist tools to understand Hitchin's generalized complex geometry.
Introduction to sigma models
Supersymmetry and the geometry for nonlinear sigma models
N=2 Superconformal algebra and mirror symmetry
A physicist approach to generalized complex geometry
Deformation of the Virasoro algebra via the Courant bracket
Updated 14/09/2005