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.
