Mathematical Sciences: 1992 AMS-SIAM Summer Seminar on "Exploiting Symmetry in Applied and Numerical Analysis"

数学科学：1992 年 AMS-SIAM 夏季研讨会“在应用和数值分析中利用对称性”

• 批准号: 9121007
• 负责人: James Maxwell
• 金额: $ 6.31万
• 依托单位: American Mathematical Society
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-05-15 至 1994-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9121007&HistoricalAwards=false
• 关键词: Mathematical; Sciences; 1992; AMS; SIAM

Symmetry plays an important role in nearly all branches of science. This is particularly evident in theoretical physics, where representation theory has long been a primary tool. Symmetry aspects have only recently been exploited in certain branches of mathematics. In particular, symmetry has only begun to be exploited in any systematic way in numerical analysis. In applied analysis, the study of symmetry is much more well- developed. In the area of classical differential equations, the understanding of symmetry groups as a central tool has been realized since the last century. In the relatively more recent area of bifurcation theory, symmetry has been exploited systematically only in recent years. There is a growing collection of researchers in numerical analysis who are currently attempting to use symmetry groups as a fundamental tool in their work. This project will support the 1992 AMS-SIAM Summer Seminar in Applied Mathematics to be held from July 26 - August 1, 1992 at Colorado State University. The topic of this conference (the twenty-second in this series) is Exploiting Symmetry in Applied and Numerical Analysis. The major aim of the conference is to provide a wide-ranging survey of the exploitation of symmetry in applied and numerical analysis. A purpose of the seminar is to stimulate interaction between aspects of applied mathematics (e.g., partial differential equations, integral equations, bifurcation), numerical mathematics (e.g., numerical linear algebra, boundary and finite element methods), core mathematics (e.g., representation theory of groups), and classical physics (e.g., Taylor and Benard problems). The seminar will have both an entry level summer school component intended for junior researchers and a frontier research level aspect.

对称在几乎所有的科学分支中都起着重要的作用。这在理论物理学中尤其明显，表征理论长期以来一直是理论物理学的主要工具。对称方面直到最近才在某些数学分支中得到利用。特别是，在数值分析中，对称性才刚刚开始以系统的方式被利用。在应用分析中，对称性的研究要发达得多。在经典微分方程领域，对称群作为核心工具的理解自上个世纪以来已经实现。在相对较新的分岔理论领域，对称性只是在最近几年才被系统地利用。在数值分析领域，有越来越多的研究人员正在尝试将对称群作为他们工作中的基本工具。该项目将支持于1992年7月26日至8月1日在科罗拉多州立大学举行的1992年AMS-SIAM夏季应用数学研讨会。本次会议（本系列的第22次会议）的主题是在应用和数值分析中利用对称性。会议的主要目的是对应用和数值分析中对称性的利用进行广泛的调查。研讨会的目的是激发应用数学（如偏微分方程、积分方程、分岔）、数值数学（如数值线性代数、边界和有限元方法）、核心数学（如群的表示理论）和经典物理（如泰勒和贝纳德问题）之间的相互作用。研讨会将包括初级研究人员的入门级暑期学校部分和前沿研究水平方面。