My talk will concern the application of generalized geometry to the AdS5/CFT4 correspondence in type IIB string theory. This new type of geometry makes it possible to study the most general supersymmetric AdS5 solution (with non-zero D3-brane charge). I will define the notion of ``generalized Sasaki-Einstein'' geometry, which consists of a contact structure described by a system of three symplectic forms on the 4d leaf space of the associated Reeb foliation. The contact volumes of such generalized SE manifolds can be determined by a minimization procedure. This is the geometric counterpart of a-maximization to determine the R-symmetry, and hence the central charge, in N=1 superconformal field theories. As an illustration, I will present a new infinite family of mass-deformed generalized conifold theories.