Generalized complex and Kähler geometry

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Generalized complex geometry is a unified approach to two separate fields: Symplectic geometry, used for classical mechanics, and Complex geometry, used for studying the behaviour of algebraic equations in arbitrary dimension. Besides unifying these two clasically separate disciplines, it also includes a family of intermediate geometries which are wholly new. These geometries turn out to provide alternative backgrounds for quantum field theories called "Flux compactifications", and hence are relevant to high-energy physics. The proposal has three related aims. First, to study the theoretical properties of these intermediate generalized complex structures, to form a more complete understanding of their intrinsic nature. Second, to pursue constructions of many examples of these intermediate geometrical structures. Lastly, to strengthen connections between generalized complex geometry and other fields of mathematics, such as Poisson geometry, geometry of 4-manifolds, and non-commutative geometry.