In addition to its own ongoing internal development and its basic role in other areas of mathematics (number theory, differential equations, probability, statistics), physics and chemistry (visible light and infrared optics, crystallography, wave phenomena), financial analysis (time series), medicine (tomography, brain and heart wave analysis), and biological signal processing, harmonic analysis has made fundamental contributions to essentially all twentieth century technology-based human endeavors. This includes telephone, radio, television, radar, sonar, satellite communications, medical imaging, the internet, and multimedia. This ubiquitous nature of the subject will be the focus of the second half of the ASI, where many of the most profound applications will be presented.

Thus, the ASI will not only promote the infusion of new mathematical tools into applied harmonic analysis, but will also fuel the development of applied mathematics by providing opportunities for young engineers, mathematicians, and other scientists to learn more about problem areas in today's technology that might benefit from new mathematical insights. Hence, this interdisciplinary ASI will recreate the dynamic interaction between engineers, mathematicians, and other scientists that occurred at Dr. Byrnes' four previous ASI's.

As can be seen in the list of lecturers, many of the world's leading experts in the field have agreed to be Lecturers at the ASI. Their multidisciplinary backgrounds will create a forum for interaction among academics and industrial scientists in the various technical areas indicated by the lecture titles. The initial portion of the schedule emphasizes the underlying mathematics, while the remainder of the ASI is focused around specific important applications to real-world problems.

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 harmonic analysis, 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.

Numerous giants in the field, including about half of the lecturers, have recently retired or will do so in the near future. A major purpose of the ASI is to afford them the opportunity to join together to share their profound wisdom with the many future stars of pure and applied harmonic analysis. A second purpose is to 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 twenty-first century harmonic analysis.