Mathematical Sciences: An Interdisciplinary Program in Mathematics and Physics

9627351 Deligne这笔赠款支持数学和物理之间的交叉学科计划。该计划的中心是量子场论，特别是弦理论的当前和预期的发展，以及表达和深化这些理论所需的数学。核心问题是，尽管有强有力的迹象表明，不同的弦理论是一个整体，但物理学家们还不知道这一理论应该用什么术语来表述；这有待新的物理思想和新的数学结构的结合。在理论物理中要追求的主题包括电磁二元性、超重力、弦理论的非经典对称性、场论中的孤子解以及四维的量子规范动力学。在数学方面，Calabi-Yau三重流形和可微四重流形的镜像对称性是要研究的主题之一。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方面的博士后研究员，他们可以用对方的直觉和观点来看待问题。对女性申请者将给予特别鼓励。该项目由数学和物理科学局内的数学科学处、物理处和多学科活动办公室(OMA)共同资助。(OMA为属于单一司正常职责范围内的多学科提案提供了便利，提供了一个适当的场所供其审议。)

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.)