Harmonic analysis of Laplacians in curved spaces

弯曲空间中拉普拉斯算子的调和分析

• 批准号: DP220100285
• 负责人: A/Prof Ji Li
• 金额: $ 26.48万
• 依托单位: Macquarie 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: 2022-05-02 至 2025-05-01
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP220100285
• 关键词: Harmonic; analysis; Laplacians; curved; spaces

Harmonic Analysis is a branch of mathematics which is interrelated to other fields of mathematics like complex analysis, number theory and partial differential equations (pdes) with many applications in engineering and technology. This project aims to solve a number of difficult fundamental problems at the frontier of harmonic analysis in understanding Laplacians in curved spaces. Such Laplacians control the propagation of heat and waves on manifolds and Lie groups, arising in mathematical physics and quantum mechanics. Expected outcomes are the solutions of dispersive equations and the framework of singular integrals in curved spaces; new ideas and techniques in harmonic analysis developed; and training of Australian future mathematicians.

调和分析是数学的一个分支，它与复分析、数论、偏微分方程等数学领域密切相关，在工程技术中有着广泛的应用。这个项目旨在解决一些困难的基本问题，在调和分析的前沿理解拉普拉斯在弯曲空间。这种拉普拉斯算子控制着热和波在流形和李群上的传播，出现在数学物理和量子力学中。预期成果是色散方程的解决方案和弯曲空间中奇异积分的框架;发展调和分析的新思想和技术;以及培训澳大利亚未来的数学家。