Arya Yae

My doctoral research focused on understanding the relationships between the hyperkähler metrics on 4n-dimensional manifolds. These metrics do not have explicit descriptions, but are rather realized as gauge-theoretic quotients. This means each point in the manifold corresponds to a solution to a nonlinear and nonhomogeneous PDE, and the geometric properties (curvature, geodesics, cohomology, etc.) must be understood in terms of families of solutions parameterized by boundary data. As gauge theory lies in the intersection of many mathematical disciplines, completing my thesis required a deep understanding of algebraic and differential geometry, topology, Morse theory, PDE theory, and functional analysis. My papers are listed under Publications, and you can also find slides for some Talks I gave about my research.

Recently, I have been interested in numerical analysis of equations arising from Hamiltonian dynamics and the cohomological properties of reduced phase spaces. I am actively working to produce interactive explainers of advanced research topics made for a general audience. For example, see this interactive hyperpolygon simulation.

While at the University of Oregon, I developed and taught fifteen math courses including Calculus, Linear Algebra, Multivariable Calculus, Discrete Math, and Intro to Proof. I also graded for advanced undergraduate courses such as Intro Topology, Intro to Real Analysis, and Advanced Statistical Methods. As part of the math department’s annual Directed Reading Programs, I mentored one student doing a project on set theory, and a pair of students doing a project on heat flow, Ricci flow, and geodesics.

I was a recipient of the UO Math department’s Anderson Teaching Award (2024), Anderson Research Award (2023), Civin Award (2020). I also received NSF RTG summer fellowships in 2021, 2023, 2024, and 2025.