Collaborative Research: Chromatic homotopy theory and open string theory

合作研究：色同伦理论和开弦理论

• 批准号: 0705381
• 负责人: Eric Sharpe
• 金额: $ 8.11万
• 依托单位: Virginia Polytechnic Institute and State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-06-15 至 2011-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0705381&HistoricalAwards=false
• 关键词: Collaborative; Research; Chromatic; homotopy; theory

AbstractAward: DMS-0705233, 0705381Principal Investigator: Matthew Ando, Eric R. SharpeAndo and Sharpe will investigate several questions in ellipticcohomology suggested by the physics of open string theory. Inphysics, elliptic genera arise in closed string theory, but therecent work of Stolz and Teichner and of Borisov and Libgover andGanter strongly suggests that open string theory plays animportant role in elliptic cohomology. Ando and Sharpe propose tointroduce recent developments in open string theory, particularlyideas about D-branes and K-theory, to the study of ellipticcohomology. For example they hope to use open string theory toinvestigate the relationship between elliptic cohomology and theK-theory of K-theory, as studied by Baas, Dundas, Richter, andRognes. They also hope to give a unified account of the McKaycorrespondence for elliptic genera, due to Borisov and Libgober,and for sheaves, due to Bridgeland, King, and Reid.Elliptic cohomology arises from topology, and it signals aprofound relationship between physics, particularly the physicsof string theory, and at least two branches of mathematics,topology and number theory. Precisely how these things arerelated through elliptic cohomology remains mysterious: thephysicist Edward Witten called elliptic cohomology "a piece of21st century mathematics that happened to fall into the 20thcentury." Until very recently, the study of the physics ofelliptic cohomology has focused mainly on "closed" string theory,in which particles are replaced by loops of string. There is nowa rich theory of "open" strings, in which particles may also beunlooped strands of string. Ando and Sharpe suggest that thephysics of open string theory has deep implications in ellipticcohomology. They propose to investigate several of theseimplications, which they hope will shed light on some of theimportant mysteries in the subject.

Abstractaward：DMS-0705233，0705381原理研究者：Matthew Ando，Eric R. Sharpeando和Sharpe将研究开放式弦乐理论的物理学建议的椭圆仪学中的几个问题。 不合理的，椭圆形属出现在封闭的弦理论中，但是Stolz和Teichner以及Borisov和Libgover和Libgover和Ganter的其他工作强烈地表明，开放式弦乐理论在椭圆形的共同体中扮演着动漫的角色。安多（Ando）和夏普（Sharpe）提出了开放式弦乐理论的最新发展，尤其是关于d-branes和k理论的椭圆学研究研究。 例如，他们希望使用开放式的弦理论来研究椭圆形的共同体和K理论的Thek理论之间的关系，如Baas，Dundas，Richter，Andrognes所研究。 他们还希望通过Borisov和Libgober引起的椭圆形属的McKaycorress，以及由于Bridgeland，King和Reid而引起的绵羊，纤维化的共同体学源于拓扑​​结构，IT信号源于物理学之间的关系，尤其是物理学的弦理论，以及至少两个分支机构，以及两种数学的理论，以及数学上的数字和数字。 确切地说，这些事物是如何通过椭圆形的共同体来构成的：尸体学家爱德华·维滕（Edward Witten）称为椭圆形的共同体，“恰好落入20世纪的21世纪数学片段”。 直到最近，对ellip骨共同体物理学的研究主要集中在“封闭”的弦理论上，其中粒子被弦的循环取代。 诺瓦有丰富的“开放”字符串理论，其中粒子也可能是弦的绳子。 安多（Ando）和夏普（Sharpe）表明，开放式弦理论的物理对椭圆期具有深厚的影响。 他们建议调查其中一些象征，他们希望这将阐明该主题中一些重要的奥秘。