"Symplectic topology, generalized geometry and applications"

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My research program lies in the field of differential geometry, an area of pure mathematics, which studies certain kinds of geometrical shapes and configurations of these shapes. It is intimately related to the physical world, since the descriptions of physical systems, both classical and quantum systems, often require geometrical shapes with certain special properties. Mathematically, such properties are extra structures on or symmetries of these shapes, or relations among shapes of different types. The mathematical study of these properties would help the understanding of the corresponding physical systems. More specifically, my program concerns symplectic manifolds, Lagrangian submanifolds, and generalized geometry initiated by Hitchin.