I am an Instructor in the Department of Mathematics at Princeton University, mentored by Sun-Yung Alice Chang and Paul Yang. I received my Ph.D. in Mathematics from University of California, Berkeley in 2023. I was glad to be advised by Song Sun.
I co-organize Princeton Differential Geometry and Geometric Analysis (DGGA) seminar.
My research lies in differential geometry, with a particular focus on the moduli space of Einstein 4-manifolds. I am particularly interested in boundary value problems for Einstein manifolds, including
Poincaré–Einstein 4-manifolds
Hyperkähler 4-manifolds, and more broadly, Riemannian manifolds with special holonomy
Here is my CV.
Email: hongyil at princeton dot edu
Office: Fine 910
Poincaré–Einstein 4-manifolds with conformally Kähler geometry (with Mingyang Li), preprint arXiv:2510.04928.
A short proof of the surjectivity of the period map on K3 manifolds, preprint arXiv:2304.09501.
A compactness theorem for hyperkähler 4-manifolds with boundary, Duke Mathematical Journal, 173(6):1177–1225, 2024. (link)
Locally removable singularities for Kähler metrics with constant holomorphic sectional curvature (with Si-en Gong and Bin Xu), Proceedings of the AMS, 148(5):2179–2191, 2020. (link)