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: 0504539
• 负责人: Nora Ganter
• 金额: $ 8.47万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-08-01 至 2007-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0504539&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.

项目主要研究椭圆上同性与其他数学和物理领域的相互作用，重点研究等变现象和幂运算。讨论的主题从弦理论中的轨道模型到两范畴的表示和特征理论，再到广义的Moonshine和稳定同伦理论。Hopkins-Kuhn-Ravenel特征理论是在同伦理论的背景下产生的，并揭示了上述领域之间的许多形式相似性。这些项目的目标是更好地理解这些观察结果背后的机制。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Moonshine的扭曲Hecke算子联系起来。本项目将进一步探讨这些联系，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来说：椭圆上同论是数学和物理领域的一个丰富的组合，表面上看它们之间似乎没有太多的联系。特别是在一组对称性的作用下，人们可以在看似不相关的研究领域之间观察到许多类比。与来自不同数学领域的合作者一起，该项目试图找到这些现象背后更深层次机制的解释。