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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.
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Advanced Study Institute
