Jiyuan Han, Ph.D.

About

I am an Assistant Professor of Mathematics in the Institute for Theoretical Sciences at Westlake University, where I have been since September 2021. I am a member of the Differential Geometry Group.

Before joining Westlake, I was a Golomb Visiting Assistant Professor of Mathematics at Purdue University (2018–2021). I received my Ph.D. in Mathematics from the University of Wisconsin–Madison in 2018, under the supervision of Jeff A. Viaclovsky.

Research Interests

My research lies in Differential Geometry, with a particular focus on Kähler Geometry. I am interested in canonical metrics on Kähler manifolds, including Kähler–Einstein metrics, Kähler–Ricci solitons, weighted constant scalar curvature Kähler (cscK) metrics, and scalar-flat Kähler ALE surfaces. My work studies the connections between geometric PDEs, algebraic stability conditions, and degenerations of algebraic varieties, often through the lens of the Yau–Tian–Donaldson conjecture and its generalizations.

Publications

Preprints

1. Stable Degenerations of log Fano Fibration Germs
   Jiyuan Han, Minghao Miao, Lu Qi, Linsheng Wang, Tong Zhang
   arXiv:2603.09269 2026
2. G-uniform Weighted K-stability for Models on klt Varieties
   Jiyuan Han, Yaxiong Liu
   arXiv:2506.18039 2025
3. Variation of Kähler–Einstein Metrics with Mixed Singularities
   Xin Fu, Jiyuan Han, Yongpan Zou
   arXiv:2508.02212 2025

Journal Articles

1. On the Existence of Weighted-cscK Metrics
   Jiyuan Han, Yaxiong Liu
   Advances in Mathematics Vol. 463, Article 110125 2025
   arXiv
2. Algebraic Uniqueness of Kähler–Ricci Flow Limits and Optimal Degenerations of Fano Varieties
   Jiyuan Han, Chi Li
   Geometry & Topology Vol. 28, No. 2, pp. 539–592 2024
   arXiv DOI
3. On the Yau–Tian–Donaldson Conjecture for Generalized Kähler–Ricci Soliton Equations
   Jiyuan Han, Chi Li
   Communications on Pure and Applied Mathematics Vol. 76, No. 9, pp. 1793–1867 2023
   arXiv DOI
4. Existence and Compactness Theory for ALE Scalar-flat Kähler Surfaces
   Jiyuan Han, Jeff A. Viaclovsky
   Forum of Mathematics, Sigma Vol. 8, e1 2020
   arXiv DOI
5. Local Moduli of Scalar-flat Kähler ALE Surfaces
   Jiyuan Han, Jeff A. Viaclovsky
   arXiv:1809.07233 2018
   arXiv
6. Deformation Theory of Scalar-flat Kähler ALE Surfaces
   Jiyuan Han, Jeff A. Viaclovsky
   American Journal of Mathematics Vol. 141, No. 6, pp. 1547–1589 2019
   arXiv

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