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Abstract: Mirror symmetry predicts a duality between
complex and symplectic geometry. In particular the conjecture
relates (in Kontsevich's version) sheaf cohomology of vector bundles with Floer theory of Lagrangian submanifolds. I will discuss some of the ideas behind the conjecture, such as the definition of a Lagrangian submanifold, and some recent work on the mirror analog of deformation of vector bundles which, as suggested by Fukaya-Oh-Ono-Ohta, corresponds to smoothing singularities of the Lagrangians.
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