SM: A Conference Series on Mathematical String Theory

SM：数学弦理论会议系列

• 批准号: 0963840
• 负责人: Ron Donagi
• 金额: $ 6万
• 依托单位: University of Pennsylvania
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-01 至 2012-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0963840&HistoricalAwards=false
• 关键词: SM; Conference; Series; Mathematical; String

For mathematics, string theory has been a source of many significant inspirations, ranging from Seiberg-Witten theory in four-manifolds, to enumerative geometry and Gromov-Witten theory in algebraic geometry, to work on the Jones polynomial in knot theory, and to recent progress in the geometric Langlands program and the development of derived algebraic geometry and n-category theory. In the other direction, mathematics has provided physicists with powerful tools, ranging from powerful differential geometric techniques for solving or analyzing key partial differential equations, to toric geometry, to K theory and derived categories in D-branes, to the analysis of Calabi-Yau manifolds and string compactifications, and to the use of modular forms and other arithmetic techniques. The depth, power, and novelty of the results obtained in both fields thanks to their interaction is truly mind boggling.This project initiates a biennial series of large meetings bringing together mathematicians and physicists who work on ideas related to string theory. The nature of interactions between mathematicians and physicists has been thoroughly transformed in recent years. String theory, as well as quantum field theory, has contributed a series of profound ideas which gave rise to entirely new mathematical fields and revitalized older ones. By now there is a large and rapidly growing number of both mathematicians and physicists working at the string-theoretic interface between the two academic fields. The influence flows in both directions, with mathematical techniques and ideas contributing crucially to major advances in string theory. Our conference will stimulate further research in both fields, and will help establish and deepen the interactions between them.

对于数学来说，弦理论是许多重要灵感的来源，从四流形中的Seiberg-Witten理论，到代数几何中的计数几何和Gromov-Witten理论，到纽结理论中的Jones多项式，以及几何朗兰兹程序的最新进展和衍生代数几何和n-范畴理论的发展。另一方面，数学为物理学家提供了强大的工具，从用于求解或分析关键偏微分方程的强大的微分几何技术，到环面几何，到K理论和D-膜中的派生范畴，到Calabi-Yau流形和弦紧凑化的分析，以及模形式和其他算术技术的使用。由于它们的相互作用，在这两个领域获得的结果的深度、力量和新颖性确实令人难以置信。这个项目发起了两年一次的大型会议系列，将致力于弦理论相关想法的数学家和物理学家聚集在一起。近年来，数学家和物理学家之间相互作用的性质发生了彻底的变化。弦理论和量子场论都贡献了一系列深刻的思想，这些思想催生了全新的数学领域，并使旧的数学领域重新焕发活力。到目前为止，有大量的数学家和物理学家在这两个学术领域之间的弦理论界面上工作，而且数量迅速增加。这种影响是双向的，数学技术和思想对弦理论的重大进步起到了至关重要的作用。我们的会议将促进这两个领域的进一步研究，并将有助于建立和深化它们之间的互动。