Program in Geometry of String Theory

弦论几何程序

• 批准号: 0443699
• 负责人: Mikhail Kapranov
• 金额: $ 5万
• 依托单位: Yale University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-12-15 至 2005-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0443699&HistoricalAwards=false
• 关键词: Program; Geometry; String; Theory

AbstractAward: DMS-0443699Principal Investigator: Mikhail KapranovWe propose to run a year-long program at the Fields Institute onthe subject of ``Geometry of string theory''. The program willbe devoted to mathematical subjects motivated by string theory,and to recent developments in string theory and related physicalfields which are of strong mathematical interest. On themathematical side, the aim is to foster interaction between suchareas of mathematics as derived categories, elliptic cohomology,geometric Langlands correspondence, quantum cohomology,differential geometry varieties with special holonomy and ofspecial Lagrangian varieties. On the more physical side, the aimis to foster new progress in the continuing drive towardsunderstanding the foundations of string/M-theory, and in thewealth of new ideas involving D-branes, BPS states and variousdualities which are of great importance to mathematical subjectssuch as algebraic geometry.The overall goal of the program is to advance our understandingof the fundamental questions of physics of themicroworld. Probably the most promising application of quantumphysics contemplated nowadays is the Quantum Computing Projectwhich can potentially lead to creation of computers whose powerexceeds the present-day limits by many orders of magnitude. Thisdirection is a part of the proposed activitie and we plan to havea distinguished lecture series (the Blyth Lectures) devoted tothe subject. This program represents an excellent opportunityfor young scholars to experience a high-level interdisciplinarycollaboration. In particular, it is going to be a very importanttraining ground for young American scientists.

摘要奖项：DMS-0443699首席研究员：米哈伊尔·卡普拉诺夫我们建议在菲尔兹研究所开展为期一年的项目，主题为“弦理论的几何”。 该项目将致力于由弦理论推动的数学科目，以及弦理论和具有强烈数学兴趣的相关物理领域的最新发展。在数学方面，其目的是促进数学领域之间的相互作用，例如派生范畴、椭圆上同调、几何朗兰兹对应、量子上同调、具有特殊完整性的微分几何簇和特殊拉格朗日簇。在物理方面，目的是在不断理解弦/M理论基础的过程中，以及在涉及D-膜、BPS态和各种对偶性的新思想财富中促进新的进展，这些新思想对代数几何等数学学科非常重要。该项目的总体目标是促进我们对微观世界物理学基本问题的理解。当今所考虑的量子物理学最有前途的应用可能是量子计算项目，该项目有可能创造出性能超出当今限制许多数量级的计算机。这个方向是拟议活动的一部分，我们计划举办一个专门针对该主题的杰出讲座系列（布莱斯讲座）。 该项目为年轻学者提供了体验高水平跨学科合作的绝佳机会。 特别是，它将成为美国年轻科学家非常重要的训练场。