Problems in harmonic analysis: decoupling and Bourgain-Brezis inequalities

调和分析中的问题：解耦和布尔干-布雷齐斯不等式

• 批准号: FT200100399
• 负责人: A/Prof Po-Lam Yung
• 金额: $ 63.01万
• 依托单位: The Australian National University
• 依托单位国家: 澳大利亚
• 项目类别: ARC Future Fellowships
• 财政年份: 2020
• 资助国家: 澳大利亚
• 起止时间: 2020-10-29 至 2024-10-28
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/FT200100399
• 关键词: Problems; harmonic; analysis; decoupling; Bourgain

This project in mathematics aims to study two recent, promising developments in harmonic analysis, namely Fourier decoupling and Bourgain-Brezis inequalities. The former captures how waves interfere upon superposition; the latter arose initially in the study of the Ginzburg-Landau theory of superconductors. This exciting project seeks to deliver deep insights into how different frequencies interact, and aims to develop powerful new tools to advance the study of partial differential equations and analytic number theory. This Future Fellowship should benefit Australia by improving our scientific capability. It will bring world-class researchers to Australia for collaboration, and put Australia at the forefront of first rate research.

这个数学项目的目的是研究调和分析中两个最近的，有前途的发展，即傅立叶解耦和Bourgain-Brezis不等式。前者描述了波在叠加时是如何干涉的;后者最初是在研究金兹伯格-朗道超导理论时出现的。这个令人兴奋的项目旨在深入了解不同频率如何相互作用，并旨在开发强大的新工具来推进偏微分方程和解析数论的研究。这个未来的奖学金应该有利于澳大利亚提高我们的科学能力。它将为澳大利亚带来世界一流的研究人员进行合作，并将澳大利亚置于一流研究的前沿。