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

主要研究者：James S Byrnes提案编号：DMS-0327088机构：私营，纽波特RITle：北约计算非交换代数高级研究所和 应用摘要几何代数在几何学中最重要的应用之一是它用于表示欧几里得和闵可夫斯基旋转群。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，开始与工作的伯恩赛德，弗罗贝纽斯和舒尔，一直受到影响，甚至更普遍的问题。因此，一般群作用为群论中的强大方法以及在物理、化学、分子生物学和信号处理中使用群提供了基础。这些方面，也将详细介绍了许多校长讲师。代数，分析和几何的融合，以及它们在真实的世界问题中的应用，已经成为世纪以来数学的主导主题。几何代数，介绍和分类的克利福德在世纪后期，发挥了突出的作用，在这方面的努力，看到在数学工作的嘉当，布劳尔，外尔，舍弗利，阿蒂亚，和博特，并在应用物理学的工作泡利，狄拉克和其他人。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的不断扩大的概念和计算需求的关键工具，因为它迅速增长的重要性。信号和图像处理用于遥感，微型和无人驾驶车辆，生物处理以及神经和量子计算。意大利空间局将汇集来自学术界和工业界的具有广泛多学科背景的世界领导人参加一个互动论坛;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，更多地了解问题领域，以及在这一至关重要和不断增长的纯科学和应用科学领域中公认的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的人提供这些见解。 意大利空间研究所和会议记录的一个主要特点是提出将构成二十一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.