Interactions of Elliptic Cohomology with Other Subjects

椭圆上同调与其他学科的相互作用

• 批准号: 0754204
• 负责人: Nora Ganter
• 金额: $ 4.01万
• 依托单位: Colby College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-08-15 至 2008-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0754204&HistoricalAwards=false
• 关键词: Interactions; Elliptic; Cohomology; Other; Subjects

AbstractAward: DMS-0504539Principal Investigator: Nora GanterThe project investigates the interaction of elliptic cohomologywith other areas of mathematics and physics, with a focus onequivariant phenomena and power operations. Subjects treatedrange from orbifold models in string theory over representationand character theory in 2-categories to generalized Moonshine andstable homotopy theory. Hopkins-Kuhn-Ravenel character theoryarose in the context of homotopy theory and exposes many formalsimilarities between the above fields. The goal of the projectis to better understand the mechanisms underlying theseobservations. Power operations in elliptic cohomology werealready linked to product formulas in string theory and to thetwisted Hecke operators of generalized Moonshine. This projectwill further pursue these connections, aiming to clarify thelinks between the literature in these three subjects.In less technical terms: Elliptic cohomology is a rich mix ofareas of mathematics and physics, which on the surface do notappear to have much to do with each other. Especially in thepresence of an action by a group of symmetries, one can observemany analogies between seemingly unrelated research areas. Withcollaborators from various fields of mathematics, this projectseeks to find an explanation for the deeper mechanisms underlyingthese phenomena.

摘要奖：DMS-0504539主要研究员：诺拉·甘特该项目研究椭圆上同调与其他数学和物理领域的相互作用，重点是等变现象和幂运算。讨论的范围从弦理论中关于表征的奥比福尔德模型和2-范畴中的特征标理论到广义的月光理论和稳定同伦理论。霍普金斯-库恩-拉弗内尔特征标理论是在同伦理论的背景下提出的，揭示了上述领域之间的许多形式上的相似之处。该项目的目标是更好地理解这些观测背后的机制。椭圆上同调中的幂运算已经与弦理论中的乘积公式和广义Moonlight的扭曲Hecke算子联系在一起。这个项目将进一步探索这些联系，旨在澄清这三个主题的文献之间的联系。用不那么专业的术语：椭圆上同调是数学和物理领域的丰富组合，表面上看这两个领域似乎没有太大关系。特别是在一组对称性的作用下，人们可以观察到看似无关的研究领域之间的许多相似之处。这个项目与来自不同数学领域的合作者一起，试图为这些现象背后的更深层次机制找到一个解释。