Optimal shapes in geometry and physics: Isoperimetry in modern analysis

几何和物理学中的最佳形状：现代分析中的等周法

• 批准号: DP220100067
• 负责人: Dr Julie Clutterbuck
• 金额: $ 21.59万
• 依托单位: Monash University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2022
• 资助国家: 澳大利亚
• 起止时间: 2022-12-01 至 2024-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP220100067
• 关键词: Optimal; shapes; geometry; physics; Isoperimetry

This project will find the best isoperimetric shapes in curved spaces: shapes that optimise geometric or analytic quantities, such as the volume enclosed by a surface of a given area, or the resonant frequency of a drum of given area. The optimal shapes lead to tools that are widely used in differential equations, geometric analysis, statistical physics, probability theory, and quantum computing. Through this work, we will forge connections between the geometry of curved spaces, and the physics of operators therein. The significant benefits of this project include increasing fundamental mathematical knowledge, building capacity in Australia’s world-class geometric analysis community, and strong links with international partners.

该项目将在弯曲空间中找到最佳等周形状：优化几何或分析量的形状，例如给定面积的表面所包围的体积，或给定面积的鼓的共振频率。 最佳形状导致广泛用于微分方程，几何分析，统计物理，概率论和量子计算的工具。 通过这项工作，我们将建立弯曲空间的几何之间的联系，并在其中的运营商的物理。 该项目的重大好处包括增加基础数学知识，在澳大利亚的世界级几何分析社区的能力建设，并与国际合作伙伴的密切联系。