Mathematical Sciences: An Interdisciplinary Program in Mathematics and Physics

9627351 Deligne该基金支持数学和物理之间的交叉学科项目。该计划是围绕当前和预期的发展在量子场论，特别是弦理论，和数学需要表达和进一步这些理论的中心。核心问题是，虽然有强有力的迹象表明，不同的弦理论是一体的，但物理学家们还不明白，这一理论应该用什么术语来表述；这需要新的物理思想和新的数学结构的结合。在理论物理中要研究的课题包括电磁对偶性、超重力、弦理论的非经典对称性、场论中的孤子解和四维量子规范动力学。在数学方面，Calabi-Yau三折和可微四流形的镜像对称性是有待研究的课题之一。该计划旨在更好地使数学家和物理学家能够从其他领域的角度思考共同感兴趣的问题。因此，该计划包含一个跨学科的教育目标。研究人员将培养数学和物理学方面的博士后，他们可以用直觉和他人的观点来看待问题。对女性申请者给予特别鼓励。该项目由数学科学司、物理司以及数学和物理科学理事会下属的多学科活动办公室共同资助。（OMA通过提供适当的场所供其考虑，促进支持属于单一部门正常职责范围内的多学科提案。）

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.)