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

欧文西格尔教授是一个非常有创造力， 广泛而有影响力的数学家 他的开创性 五十年来的贡献跨越了一系列的研究 从非交换积分、算子代数、 表示论，交换和非交换调和 分析，李群，量子物理学，以及最近 河外天文学 西格尔教授的研究仍然是 最高的口径，和他的肥沃的头脑仍然是一个字体为两者 非常漂亮的数学和对 宇宙的基本物理定律 目前的建议对待数学物理的一个大的 规模 它的目的是全面研究基础物理 利用一系列复杂的数学思想 从泛函和调和分析，几何，群 非线性偏微分方程 散射理论，以及更多。 这项工作的核心是波 方程（和其他零质量方程） 时空，闵可夫斯基空间之外的解的延伸， 以及非线性波动方程的量子化。 应用 非线性抛物偏微分方程的黎曼几何 微分方程与数学建模密切相关， 经验基本粒子现象 这是一个巨大的 数学项目的重大意义，以广阔的 自然科学

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.