Mathematical Sciences: An Interdisciplinary Program in Mathematics and Physics

小行星9627351 该补助金支持数学和物理之间的接口的跨学科计划。该计划围绕量子场论，特别是弦理论，以及表达和进一步发展这些理论所需的数学的当前和预期的发展。核心问题是，虽然有强有力的迹象表明不同的弦理论是一个理论，但物理学家还不知道这个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。在理论物理学中要追求的主题包括电磁对偶性，超引力，弦论的非经典对称性，场论中的孤子解和四维量子规范动力学。在数学方面，Calabi-Yau三重流形和可微四维流形的镜像对称性是待研究的课题之一。 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。研究人员将培训数学和物理学博士后研究员，他们可以用直觉和其他人的观点来看待问题。将特别鼓励女性申请人。该项目由数学科学部、物理部和数学和物理科学局多学科活动办公室（OMA）共同资助。(The OMA通过提供一个合适的场所来考虑属于单个部门正常职责范围内的多学科提案，从而为这些提案提供支持。

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.)