NATO Advanced Study Institute on Computational Noncommutative Algebra and Applications; July 6-19, 2003; Tuscany, Italy

北约计算非交换代数及其应用高级研究所；

• 批准号: 0327088
• 负责人: James Byrnes
• 金额: $ 1.38万
• 依托单位: Byrnes James S
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-07-01 至 2004-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0327088&HistoricalAwards=false
• 关键词: NATO; Advanced; Study; Institute; Computational

Principal Investigator: James S ByrnesProposal Number: DMS- 0327088Institution: private, Newport RITitle: NATO Advanced Study Institute on Computational Noncommutative Algebra and ApplicationsAbstractOne of the most important applications of geometric algebras to geometry is its use for the representation of groups of Euclidean and Minkowski rotations. This aspect and its direct relation to robotics and vision will be discussed by several of the Principal Lecturers at the Advanced Study Institute conference. Group theory, beginning with the work of Burnside, Frobenius and Schur, has been influenced by even more general problems. As a result, general group actions have provided the setting for powerful methods within group theory and for the use of groups in applications to physics, chemistry, molecular biology, and signal processing. These aspects, too, will be covered in detail by many of the Principal Lecturers.The fusion of algebra, analysis and geometry, and their application to real world problems, have been dominant themes underlying mathematics for over a century. Geometric algebras, introduced and classified by Clifford in the late 19th century, have played a prominent role in this effort, as seen in the mathematical work of Cartan, Brauer, Weyl, Chevelley, Atiyah, and Bott, and in applications to physics in the work of Pauli, Dirac and others. The topics of the Advanced Study Institute conference, geometric algebras and computational group harmonic analysis, have emerged as key tools for resolving the ever expanding conceptual and computational demands on signal and image processing as it rapidly grows in importance. Signal and image processing is used in remote sensing, micro and unmanned vehicles, biological processing and neural and quantum computing. The ASI will bring together world leaders from both academia and industry with extensive multidisciplinary backgrounds for an interactive forum; they will initiate new efforts and intensify existing efforts towards a unified computational framework for the advancement of a broad range of applications. The forum will provide opportunities for young scientists and engineers to learn more about problem areas and about the crucial role played by new mathematical insights from recognized experts in this vital and growing area of both pure and applied science. The team-authored proceedings, to be written by the lecturers, will offer these insights to those unable to attend. A key feature of both the ASI and the proceedings will be the presentation of problems and applications that will shape the twenty-first century computational technology base.

主要研究者：James S ByrnesProposal Number: DMS- 0327088机构：private， Newport rittitle: NATO高级计算非交换代数与应用研究所摘要几何代数在几何中最重要的应用之一是它用于欧几里得和闵可夫斯基旋转群的表示。这方面及其与机器人和视觉的直接关系将在高级研究所会议上由几位首席讲师讨论。群论，从伯恩赛德、弗罗本纽斯和舒尔的工作开始，受到更普遍问题的影响。因此，一般的群体行为为群体理论中的强大方法提供了基础，并为群体在物理、化学、分子生物学和信号处理中的应用提供了基础。这些方面也将由许多首席讲师详细介绍。一个多世纪以来，代数、分析和几何的融合，以及它们在现实世界问题中的应用，一直是数学的主导主题。几何代数，由克利福德在19世纪晚期引入并分类，在这一努力中发挥了突出作用，如在Cartan， Brauer, Weyl, Chevelley， Atiyah和Bott的数学工作中，以及在泡利，狄拉克和其他人的物理工作中的应用。高级研究所会议的主题，几何代数和计算群谐波分析，已经成为解决信号和图像处理日益扩大的概念和计算需求的关键工具，因为它的重要性正在迅速增长。信号和图像处理应用于遥感、微型和无人驾驶车辆、生物处理以及神经和量子计算。ASI将汇集来自学术界和工业界的世界领导人，他们具有广泛的多学科背景，是一个互动论坛；他们将开始新的努力，并加强现有的努力，以建立统一的计算框架，促进广泛的应用。该论坛将为年轻的科学家和工程师提供机会，让他们更多地了解问题领域，以及在这个至关重要且不断发展的纯科学和应用科学领域，来自公认专家的新数学见解所发挥的关键作用。由讲师撰写的团队撰写的会议记录将为那些无法参加会议的人提供这些见解。ASI和会议的一个关键特征将是提出将塑造21世纪计算技术基础的问题和应用。