9622991 MUHLY This is a request for travel support for junior investigators and graduate students to attend the conference, Aegean Conference in Operator Algebras and Applications, that is scheduled for the period, August 17, 1996, to August 27, 1996, at the University of the Aegean. With the advent of the theory of operator spaces, also known as "quantized functional analysis", general, not-necessarily-self-adjoint, operator algebras have achieved an ontological status comparable to that held by the self-adjoint operator algebras. Although the non-self-adjoint theory is not yet as well developed, from certain perspectives, the explosion of results that has taken place in the last six years, or so, deserves to be exposed in a fashion that will allow the uninitiated, particularly younger scholars, easy access to the basics of the subject from the current perspective. The objective of the conference is to provide a series of short courses, that will be published, designed to provide an overview of the theory of non-self-adjoint operator algebras and its relation to other areas of operator algebra and modern analysis. The themes to be stressed are: non-self-adjoint operator algebras, general theory; concrete operator algebras, particularly reflexive algebras; multivariable operator theory and representations of function algebras; metric variations on themes from algebra - Hilbert and operator modules; operator spaces and their applications to Banach space theory and harmonic analysis; operator algebraic approaches to quantum groups; non-self-adjoint operator algebras and wavelets. The theory of non-self-adjoint operator algebras plays a central role in the mathematical underpinnings of a lot of mathematics applied to areas of national need. For example, in the area of signal processing, which is used to transmit data and images involved in all fields of science - from space observatories to tomographs of the brain - fundamental constructs, such as the so-calle d Toeplitz matrices and wavelet transforms, obtain their deepest significance and are most clearly revealed when viewed from the perspective of operator algebra. Operator algebra lays bare their basic algebraic properties (how they are manipulated in practice) and metric properties as well (how they are measured). In oil exploration, which involves wavelets and signal processing in a somewhat different fashion, operator algebraic methods, known as commutant lifting play a fundamental role. Also, in control theory, particularly in the design of aircraft and noise abaters, the mathematics involved is to a large extent operator algebra. The breakthrough that took place about six years ago, and alluded to above, enables the practitioner of this field to bring to bare effectively the full power of modern algebra to tackle the most basic and fundamental structural questions. The advances in this field have been very exciting and more are to come. But it is time collect a summary of what is known, including bibliographies, so that new people can enter this exciting, emerging field of research.
