Spectral Zeta Invariants of Riemannian Manifolds

黎曼流形的谱 Zeta 不变量

• 批准号: 0902234
• 负责人: Kate Okikiolu
• 金额: $ 15.2万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-15 至 2011-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0902234&HistoricalAwards=false
• 关键词: Spectral; Zeta; Invariants; Riemannian; Manifolds

Understanding the relationship between the geometry of a space and the spectra of natural geometric differential operators on the space is a problem which arises in a number of branches of science. Individual eigenvalues are hard to analyze and often the geometry of a space is more clearly reflected by certain weighted averages of the eigenvalues such as zeta invariants. Okikiolu is proposing to study both the general theory of zeta invariants and special cases which are of particular physical and geometrical relevance.The purpose of this research is to increase our understanding of the geometric significance of zeta invariants for future physical and geometrical applications.Okikiolu proposes to continue to make her research accessible to undergraduates through student seminars and colloquia, and to further integrate research into the undergraduate experience. She seeks to:a) motivate course material with accessible examples and calculations taken from her own research,b) create opportunity for students to collaborate on building proofs in the classroom,c) foster collaborative intellectual curiosity.This will hopefully produce students who have a deeper understanding and appreciation for the subject.

理解空间几何和空间上自然几何微分算子的谱之间的关系是一个出现在许多科学分支中的问题。 单个特征值很难分析，通常空间的几何形状更清楚地反映在特征值的某些加权平均值上，例如zeta不变量。 Okikiolu建议研究zeta不变量的一般理论和特殊情况下，这是特殊的物理和几何相关性。这项研究的目的是增加我们的理解几何意义的zeta不变量为未来的物理和几何应用。Okikiolu建议继续使她的研究，通过学生研讨会和座谈会本科生访问，并进一步将研究融入本科生的经历。她的目标是：a）用她自己研究中的例子和计算来激励课程材料，B）为学生创造在课堂上合作建立证明的机会，c）培养合作的求知欲。这将有望培养对该主题有更深理解和欣赏的学生。