ARC Future Fellowships - Grant ID: FT210100405

积分变换与模理论。这个项目是代数几何，纯数学的一个分支。一个最重要的目标是更好地理解数学中普遍存在的分类问题及其在物理学中的应用\n中出现的复杂几何问题所\n涉及的代数。然后，这些新知识将被应用于进一步阐明这些空间的几何。这个项目的预期成果包括我们通过傅里叶-穆凯变换对代数堆栈派生范畴的理解取得的重大进展。

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.