Mathematical Sciences: An Interdisciplinary Program in Mathematics and Physics

数学科学：数学和物理的跨学科项目

• 批准号: 9627351
• 负责人: Pierre Deligne
• 金额: $ 60万
• 依托单位: Institute For Advanced Study
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-09-01 至 2000-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9627351&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Interdisciplinary; Program; Mathematics

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.)

9627351 Deligne这笔赠款支持数学与物理学之间接口中的跨学科程序。该程序围绕量子场理论，尤其是弦理论的当前和预期发展，以及表达和进一步进一步发展这些理论所需的数学。核心问题是，尽管有很强的迹象表明不同的弦理论是一种，但物理学家尚未理解该理论应该制定的术语。这等待着新的物理思想和新的数学结构的结合。在理论物理学中要提出的主题包括电磁二元性，超级重力，弦理论的非古典对称性，田间理论中的孤子解决方案以及四个维度的量子量规动力学。在数学方面，要研究的主题之一是数学方面的镜子对称性三倍和可区分的四个manifolds。 该计划旨在使数学家和物理学家从另一个领域的角度考虑共同兴趣的问题。因此，该计划包含一个跨学科的教育目标。调查人员将在数学和物理学上培训博士后研究员，他们可以研究对方的直觉和观点的问题。女性申请人将受到特别的鼓励。该项目由数学科学，物理司以及数学和物理科学局内部的多学科活动（OMA）共同资助。 （OMA通过提供适当的住所来考虑的多学科建议的支持，这些建议属于单个部门的正常责任。）