NATO NATO Logo Advanced Study Institute 
Computational Noncommutative Algebra
and Applications
July 6--19, 2003
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Meeting Purpose
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. One of the most important applications of geometric algebras to geometry is to 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.

Moreover, 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.

With the rapidly growing importance of, and ever expanding conceptual and computational demands on signal and image processing in remote sensing, computer vision, medical image processing, and biological signal processing, and on neural and quantum computing, geometric algebras, and computational group harmonic analysis, the topics of the proposed ASI have emerged as key tools. The list of fully committed principal speakers includes many of the world's leading experts in the development of new algebraic modeling and signal representation methodologies, novel Fourier-based and geometric transforms, and computational algorithms required for realizing the potential of these new application fields.

The ASI will bring together these world leaders from both academia and industry, with extensive multidisciplinary backgrounds evidenced by their research and participation in numerous workshops and conferences. This will create an interactive forum for initiating new and intensifying existing efforts aimed at creating a unified computational noncommutative algebra for advancing the broad range of applications indicated above. The forum will provide opportunities for young scientists and engineers to learn more about these problem areas, and the vital role played by new mathematical insights, from the recognized experts in this vital and growing area of both pure and applied science.

The directors will ensure that the talks are designed to address an audience consisting of a broad spectrum of scientists, engineers, and mathematicians involved in these fields. Participants will have the opportunity to interact with those individuals who have been on the forefront of the ongoing explosion of work in computational noncommutative algebra, to learn firsthand the details and subtleties of this exciting area, and to hear these experts discuss in accessible terms their contributions and ideas for future research. Furthermore, the team-authored textbook to be written by the lecturers will offer these insights to those unable to attend.

Among the Principal Lecturers are most of the giants in the field. They will join together in this ASI to share their profound wisdom with the many future stars of pure and computational noncommutative algebra. In addition, we will produce a book for current and future generations, highlighting their thoughts and insights. A key feature of both the ASI and the book will be their presentation of problems and applications that will shape the twenty-first century computational technology base.

We wish to thank the following for their contribution to the success of this conference:
NATO Scientific & Environmental Affairs Division
DARPA Defense Sciences Office
U. S. Air Force Office of Scientific Research
U. S. Air Force European Office of Aerospace Research and Development
U. S. Air Force Rome Laboratories Sensors Directorate
U. S. Army Space and Missile Defense Command
U. S. National Science Foundation
Raytheon Company, USA
Universität Bielefeld, Germany
Universität Bonn, Germany
Melbourne University, Australia
Prometheus Inc.

Home | Getting There | Purpose | Application | Schedule | Lecturers | Posters | Participants