Cohomological invariants and perturbation problems for Fourier algebras and group algebras

傅里叶代数和群代数的上同调不变量和微扰问题

• 批准号: 402153-2011
• 负责人: Choi, Yemon
• 金额: $ 1.31万
• 依托单位: University of Saskatchewan
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=529448
• 关键词: Cohomological; invariants; perturbation; problems; Fourier

My main field of research straddles the boundary of several domains within mathematics: functional analysis, harmonic analysis, and abstract algebra. Let me try to give an overview of what some of these terms mean. Functional analysis is a branch of mathematics which originated in the early 20th century, motivated by the need to formulate and study systems of differential equations that model various physical phenomena. It has historically had close links with the branch of mathematics known as Fourier analysis, which is an ancestor of harmonic analysis, and is concerned with the study of periodic motion or signals, such as vibration in a string or an air column, or electro-magnetic waves.

我的主要研究领域跨越数学中多个领域的边界：函数分析、调和分析和抽象代数。让我试着概括一下其中一些术语的含义。泛函分析是数学的一个分支，起源于世纪早期，其动机是需要制定和研究模拟各种物理现象的微分方程系统。它在历史上与数学的分支傅立叶分析有着密切的联系，傅立叶分析是谐波分析的祖先，并且与周期运动或信号的研究有关，例如弦或空气柱的振动，或电磁波。