Spectral Zeta Invariants of Riemannian Manifolds

理解空间的几何形状和空间上的自然几何微分算子的谱之间的关系是一个在许多科学分支中出现的问题。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，如zeta不变量。Okikiolu建议研究zeta不变量的一般理论和具有特殊物理和几何相关性的特殊情况。本研究的目的是增加我们对zeta不变量在未来物理和几何应用中的几何意义的理解。Okikiolu建议继续通过学生研讨会和座谈会向本科生提供她的研究，并进一步将研究融入本科生的经历。她寻求：a)用她自己的研究中易于理解的例子和计算来激励课程材料；b)为学生创造机会，在课堂上合作建立证明；c)培养合作的求知欲。这将有希望培养出对这门学科有更深理解和欣赏的学生。

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.