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.

该项目旨在回答有关稳定条件空间拓扑的问题，在过去的二十年中，在许多不同的数学领域中已成为中心对象。 所提出的工作将在表示理论，群体理论和代数几何形状中产生重要的后果。 该项目表明，在稳定条件理论中，来自先前无关领域的工具，包括不连续的微分方程和离散的动力系统，至关重要。 潜在的好处包括分辨出数学的杰出猜想，不同数学领域之间的新联系的启动以及将机器学习技术引入数学研究。