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源泉，从四流形中的塞伯格-维滕理论，到代数几何中的枚举几何和格罗莫夫-维滕理论，到纽结理论中的琼斯多项式，以及最近的几何朗兰兹纲领的进展以及派生代数几何和 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微分几何技术，到环面几何，到K理论和D-膜中的派生类别，到卡拉比-丘的分析流形和弦紧化，以及模形式和其他算术技术的使用。由于这两个领域的相互作用而获得的成果的深度、力量和新颖性确实令人难以置信。该项目发起了两年一次的一系列大型会议，将研究弦理论相关思想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已经彻底改变。弦理论和量子场论贡献了一系列深刻的思想，催生了全新的数学领域并振兴了旧的数学领域。到目前为止，有大量数学家和物理学家致力于这两个学术领域之间的弦理论接口，而且数量正在迅速增长。这种影响是双向的，数学技术和思想对弦理论的重大进步做出了至关重要的贡献。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相互作用。