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

主要研究人员：詹姆斯·S命题编号：DMS-0327088机构：私有，纽波特：北约计算非对易代数及其应用高级研究所摘要几何代数在几何中最重要的应用之一是用它来表示欧几里德旋转和Minkowski旋转的群。这一方面及其与机器人学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。群论始于伯恩赛德、弗洛贝尼乌斯和舒尔的工作，后来受到了更普遍的问题的影响。因此，一般的基团作用为群论中的强大方法提供了环境，并为在物理、化学、分子生物学和信号处理应用中使用群提供了环境。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，是一个多世纪以来数学的主要主题。由Clifford在19世纪末引入并分类的几何代数在这一努力中发挥了突出的作用，如Cartan，Brauer，Weyl，Chevelley，Atiyah和Bott的数学工作，以及Pauli，Dirac和其他人的工作对物理的应用。高等研究院会议的主题，几何代数和计算群谐分析，已经成为解决信号和图像处理日益增长的概念和计算需求的关键工具，因为它的重要性迅速增长。信号和图像处理用于遥感、微型和无人驾驶飞行器、生物处理以及神经和量子计算。ASI将汇聚具有广泛多学科背景的学术界和工业界的世界领袖参加一个互动论坛；他们将发起新的努力，并加强现有的努力，以建立一个统一的计算框架，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，以及公认的专家在这一重要且不断增长的理论科学和应用科学领域中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过程将为那些无法出席的人提供这些见解。ASI和会议记录的一个关键特点将是提出将塑造21世纪计算技术基础的问题和应用。

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.