I am currently a Math Fellow in the Department of Mathematics at UC Irvine, mentored by Jeff Viaclovsky. I was an instructor at Princeton University during Fall 2023-Spring 2026, 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-organized Princeton Differential Geometry and Geometric Analysis (DGGA) seminar during Fall 2024-Spring 2026.
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: hongyi.liu@uci.edu
Poincaré–Einstein 4-manifolds with cusps (with Mingyang Li), preprint arxiv:2605.25462.
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)