ARC Future Fellowships - Grant ID: FT210100405

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Integral transforms and moduli theory. This project is in algebraic geometry, a branch of pure\nmathematics. An overarching goal is a better understanding of the\nalgebra underlying the sophisticated geometries that arise in the\nclassification problems that are pervasive in mathematics and its\napplications to physics. This new knowledge will then be applied to\nfurther elucidate the geometry of these spaces. \n\t\nExpected outcomes of this project include major progress in our\nunderstanding of derived categories of algebraic stacks via the\nFourier-Mukai transform.\n\nThe benefit will be to enhance the international stature of Australian\nscience.