ARC Future Fellowships - Grant ID: FT210100405

积分变换和模理论。这个项目属于代数几何，是纯数学的一个分支。首要目标是更好地理解在数学及其在物理中的应用中普遍存在的非分类问题中出现的复杂几何背后的非代数。这些新知识将被应用于进一步阐明这些空间的几何形状。该项目的预期成果包括我们通过傅里叶- mukai变换对代数堆栈派生类别的理解方面的重大进展。这样做的好处是提高澳大利亚科学的国际地位。

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.