This award supports the research in Combinatorics and Operations Research of Professor Peter Hammer of Rutgers University. Dr. Hammer's work centers on the study of pseudo- Boolean functions, which typically associate a number to each subset of a finite set. Applications in science are numerous; to name a few applications, this work has implications for minimization as in VLSI design, and Ising spin glass models and neural networks in physics. The specific goal of this project is on the one hand to gain a better understanding of pseudo- Boolean functions, with an emphasis on the construction of a coherent theory, and on the other hand to develop the compu- tational mathematics of these functions, accompanied by the implementation of efficient codes and by numerical experi- mentation. This research falls in the broad category of Combinatorics, which is one of the most active fields in today's mathematics. Fundamentally, Combinatorics represents a systematization of the very first of all mathematical activities, counting. In its modern development, however, Combinatorics has gone beyond just counting to make use of a wide variety of advanced mathematical techniques, and although its roots go back several centuries, the field has had an explosive development in the past few decades because of its importance in communications and information technology.
