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

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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.