Mathematical Sciences: Second Magma Conference on Computational Algebra; May 12-16, 1996; Milwaukee, WI

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9626327 Slattery The investigator and colleagues organize the Second Magma Conference on Computational Algebra. In the past few years a number of significant advances have taken place in several different branches of computational algebra and number theory. Because of the growing interdependence between the different branches, an algorithmic advance in one area often has a major impact on the performance of algorithms in other areas. Consequently, the meeting brings together workers from some of the key areas, including researchers working on software development as well as those using these tools. The conference is intended to inform algorithm designers and users of recent developments in cognate areas of computational algebra, number theory, and geometry and inform key theoretical mathematicians of the possibilities offered by the computational algebra tools that are now becoming available. It is also expected to identify desirable algorithm and software developments that would result in significant new applications in the near future. The conference promotes the use of the techniques of computational algebra in application areas such as digital signal processing, complex system design, network design, cryptography, coding theory and applied combinatorics. Algebra studies basic questions about discrete structure and symmetry in the world. Theoretical results from this branch of mathematics help chemists understand the spectra of organic molecules, physicists organize families of elementary particles, and engineers solve systems of equations. Algebraic invariants are used to answer biochemists' questions about knotting in DNA and anthropologists have even used algebraic classifications to organize native artifacts in the southwestern U.S. For many years mathematicians have studied algebra with little more than their imaginations and a pencil and paper. But now, computers allow researchers to work with larger and more complicated situations tha n were possible in the past. Computational algebra is the general title given to these research efforts. However, to use a computer in mathematical research requires the development of specialized software -- a task that can be time-consuming for the typical researcher. One way to address this need is through systems such as Magma which provide easy access to state-of-the-art algorithms in a number of fields of study. Another important process is to encourage researchers to share their experiences (and even software) through conferences such as this; the interaction at a conference often leads to adaptation of ideas and development of new directions. These tools enable theoretical researchers to explore more complicated situations, to gain insight in unfamiliar settings, and to compute answers to larger problems. Computer-based work on primality testing and factoring of large numbers is showing direct application to cryptography and security. Work in finite geometries and designs are providing improved techniques for error-detection and data compression. These have a large impact on everyone's use of computers and communications.