Deformation of singularities through Hodge theory and derived categories

通过霍奇理论和派生范畴进行奇点变形

• 批准号: DP240101934
• 负责人: Dr Behrouz Taji
• 金额: $ 31.71万
• 依托单位: The University of New South Wales
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2024
• 资助国家: 澳大利亚
• 起止时间: 2024-02-02 至 2027-02-01
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP240101934
• 关键词: Deformation; singularities; through; Hodge; theory

Moduli theory, the modern classification theory of mathematical objects, is a branch of algebraic geometry with applications in wide-ranging areas from the theoretical high-energy physics (dark matter and Higgs boson) to data encryption and correction via cryptography. The aim of this project is to resolve central open problems in this theory. This will be achieved by developing new methods and establishing deeper connections between various dynamic branches of these fields. By undertaking research at the forefronts of these highly active areas, this project will both strengthen the current expertise within the Australian mathematical community and precipitate the advance of Australian high-tech industries.

模理论是数学对象的现代分类理论，是代数几何的一个分支，其应用范围广泛，从理论高能物理（暗物质和希格斯玻色子）到通过密码学进行的数据加密和校正。本项目的目的是解决这一理论中的中心开放问题。这将通过开发新方法和在这些领域的各种动态分支之间建立更深层次的联系来实现。通过在这些高度活跃的领域的前沿开展研究，该项目将加强澳大利亚数学界目前的专业知识，并促进澳大利亚高科技产业的发展。