Stability conditions: their topology and applications

稳定性条件：拓扑和应用

• 批准号: DP240101084
• 负责人: Prof Anthony Licata
• 金额: $ 29.05万
• 依托单位: The Australian National University
• 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: 2024-01-01 至 2026-12-31
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP240101084
• 关键词: Stability; conditions; their; topology; applications

This project aims to answer questions about the topology of the space of stability conditions, which has emerged as a central object in a number of different mathematical areas in the past two decades. The proposed work will have important consequences in representation theory, group theory, and algebraic geometry. The project shows that tools from previously unrelated areas, including discontinous differential equations and discrete dynamical systems, are crucial in the theory of stability conditions. Potential benefits include the resolution of outstanding conjectures in mathematics, the initiation of new connections between different areas of mathematics, and the introduction of machine learning techniques into mathematical research.

该项目旨在回答关于稳定性条件空间拓扑的问题，这在过去二十年中已经成为许多不同数学领域的中心对象。所提出的工作将对表示理论、群论和代数几何产生重要影响。该项目表明，来自以前不相关领域的工具，包括不连续微分方程和离散动力系统，在稳定性条件理论中至关重要。潜在的好处包括解决数学中突出的猜想，启动不同数学领域之间的新联系，以及将机器学习技术引入数学研究。