9627351 Deligne This grant supports an interdisciplinary program in the interface between mathematics and physics. The program is centered around the current and anticipated developments in quantum field theory, especially string theory, and the mathematics needed to express and to further those theories. The central problem is that while there are strong indications that the different string theories are one, physicists do not yet understand in what terms this one theory should be formulated; this awaits a combination of new physical ideas and new mathematical structures. Among the topics to be pursued in theoretical physics are electric-magnetic duality, supergravity, non-classical symmetries of string theory, soliton solutions in field theory, and quantum gauge dynamics in four dimensions. On the mathematics side, mirror symmetry of Calabi-Yau three-folds and differentiable four-manifolds are among the topics to be investigated. The program seeks to better enable mathematicians and physicists to think about problems of common interest from the perspective of the other field. Thus the program contains an interdisciplinary educational objective. The investigators will train postdoctoral fellows in mathematics and physics who can look at problems with the intuition and perspectives of the other. Special encouragement will be given to women applicants. This project is funded jointly by the Division of Mathematical Sciences, the Division of Physics, and the Office of Multidisciplinary Activities (OMA) within the Directorate for Mathematical and Physical Sciences. (The OMA facilitates the support of multidisciplinary proposals that fall within the normal responsibilities of a single division by providing an appropriate home for their consideration.)
