Mathematical Sciences: Research in Modern Analysis Applicable to Fundamental Physical Theory

数学科学：适用于基础物理理论的现代分析研究

• 批准号: 8706094
• 负责人: Irving Segal
• 金额: --
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-01 至 1990-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8706094&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Modern; Analysis

Professor Irving Segal has been an extraordinarily creative, broad, and influential mathematical scientist. His seminal contributions spread over five decades span a range of research from the theory of noncommutative integration, operator algebras, representation theory, commutative and noncommutative harmonic analysis, Lie groups, to quantum physics, and more recently extragalactic astronomy. Professor Segal's research is still of the highest calibre, and his fertile mind remains a font for both remarkably beautiful mathematics and foundational insights into the fundamental physical laws of the universe. The current proposal treats mathematical physics on a grand scale. Its aim is a comprehensive study of fundamental physical laws utilizing a range of sophisticated mathematical ideas drawn from functional and harmonic analysis, geometry, group representations, nonlinear partial differential equations, scattering theory, and more. Central to this work is the wave equation (and other mass zero equations) in four-dimensional space-time, the extension of solutions beyond Minkowski space, and the quantization of nonlinear wave equations. Applications to the Riemannian geometry of nonlinear parabolic partial differential equations go hand in hand with modelling of empirical elementary particle phenomena. This is an immense mathematical project of great significance to a vast expanse of natural science.

欧文·西格尔教授是一位极具创造力、广泛而有影响力的数学科学家。 他的开创性贡献跨越了五十年，涵盖了一系列研究，从非交换积分理论、算子代数、表示论、交换和非交换调和分析、李群，到量子物理学，以及最近的河外天文学。 西格尔教授的研究仍然是最高水平的，他丰富的思想仍然是非常美丽的数学和对宇宙基本物理定律的基础见解的源泉。 当前的提案从宏观角度看待数学物理学。 其目标是利用泛函分析和调和分析、几何、群表示、非线性偏微分方程、散射理论等中的一系列复杂数学思想，对基本物理定律进行全面研究。 这项工作的核心是四维时空中的波动方程（和其他质量零方程）、解扩展到闵可夫斯基空间之外，以及非线性波动方程的量化。 非线性抛物型偏微分方程黎曼几何的应用与经验基本粒子现象的建模密切相关。 这是一项巨大的数学工程，对广大的自然科学领域具有重要意义。