Integral transforms and moduli theory

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This project is in algebraic geometry, a branch of pure mathematics. An overarching goal is a better understanding of the algebra underlying the sophisticated geometries that arise in the classification problems that are pervasive in mathematics and its applications to physics. This new knowledge will then be applied to further elucidate the geometry of these spaces. Expected outcomes of this project include major progress in our understanding of derived categories of algebraic stacks via the Fourier-Mukai transform. The benefit will be to enhance the international stature of Australian science.