Hongyi Liu

Hongyi Liu is an Instructor in the Department of Mathematics at Princeton University, affiliated with the School of Arts and Sciences. His research focuses on differential and complex geometry, with an emphasis on hyperkähler manifolds, K3 surfaces, and geometric analysis. He has contributed to topics such as period maps, compactness theorems, and singularities in Kähler metrics.

His work bridges algebraic geometry, topology, and mathematical physics, addressing foundational questions in geometric structures and their applications. Recent publications highlight advancements in understanding compactness properties of hyperkähler 4-manifolds and surjectivity of period maps.