Research

LLM-Assisted Research:

Beginning in August 2026, I have incorporated large language models (LLMs) into my research. The nature and extent of their contributions vary across projects. In some works, the principal ideas and arguments are developed primarily by my collaborators and me, with LLMs used mainly for exploration, verification, technical development, or exposition. In other works, LLMs contribute more substantially to the discovery and development of mathematical ideas and proofs. In every case, the authors carefully assess and verify the mathematical arguments and take responsibility for the final work. 

• Scalar curvature bounds and tangent cones for Kähler-Ricci shrinkers, with J. Zhang, arXiv:2610.05643.

• On the tangent flows of noncollapsed Ricci flow limit spaces, with B. Wang, arXiv:2610.05204.

Earlier Preprints:

• Gromov-Hausdorff limits of noncollapsed Kähler-Ricci flows and the geometry of Ricci shrinkers, with J. Zhang, arXiv:2607.25644.

• Gromov-Hausdorff convergence of time-slices of singular Ricci flows in dimension three, arXiv:2606.13301.

• Strong uniqueness and rectifiability of generalized cylindrical singularities in Ricci flow, with H. Fang, arXiv:2605.17001.

• Singular sets in noncollapsed Ricci flow limit spaces, with H. Fang, arXiv:2510.26317.

• Strong uniqueness of tangent flows at cylindrical singularities in Ricci flow, with H. Fang, arXiv:2510.20320.

• On the structure of noncollapsed Ricci flow limit spaces, with H. Fang, arXiv:2510.12398.

• Volume estimates for the singular sets of mean curvature flows, with H. Fang, arXiv:2504.09811.

Published or Accepted papers:

• On the rigidity of Ricci shrinkers, with W. Zhang, arXiv:2305.06143, to appear in Journal of the European Mathematical Society.

• Non-collapsing of Ricci shrinkers with bounded curvature, with C. Dong, Mathematische Annalen, 394, 7 (2026).

• On Kähler Ricci shrinker surfaces, with B. Wang, Acta Mathematica, Vol. 236, Issue 1 (2026), pp. 1-50.

• Uniqueness of Kähler Ricci shrinkers on toric orbifolds, with W. Zhang, The Journal of Geometric Analysis, 35, 142 (2025).

• Heat kernel on Ricci shrinkers (II), with B. Wang, Acta Mathematica Scientia, 44, 1639-1695 (2024).

• Rigidity of the round cylinders in Ricci shrinkers, with B. Wang, Journal of Differential Geometry, Vol. 127, No. 2 (2024), 817-897.

• Ancient solutions to the Kähler Ricci flow, Geometry & Topology 28 (2024), no. 7, 3257-3283. See here for stronger results.

• Rigidity of complex projective spaces in Ricci shrinkers, with W. Zhang, Calculus of Variations and Partial Differential Equations 62, 171 (2023).

• Ancient solutions to the Ricci flow with isotropic curvature conditions, with J. Cho, Mathematische Annalen, 387, 1009-1041 (2023).

• On the geometry of asymptotically flat manifolds, with X. Chen, Geometry & Topology 25(2021), no. 5, 2469-2572.

• On the structure of Ricci shrinkers, with H. Li and B. Wang, Journal of Functional Analysis, Volume 280, Issue 9, 1 May 2021, 108955.

• On the regular-convexity of Ricci shrinker limit spaces, with S. Huang and B. Wang, Journal für die reine und angewandte Mathematik (Crelle's Journal), vol. 2021, no. 771, 2021, pp. 99-136.

• Heat kernel on Ricci shrinkers, with B. Wang, Calculus of Variations and Partial Differential Equations 59, 194 (2020).

• The rigidity of Ricci shrinkers of dimension four, with B. Wang, Transactions of the American Mathematical Society 371 (2019), 6949-6972.

• Ricci flow on asymptotically Euclidean manifolds, Geometry & Topology 22 (2018), no. 3, 1837-1891.

• Genus one open books with non-left-orderable fundamental group, with L. Watson, Proceedings of the American Mathematical Society 142 (2014), no. 4, 1425-1435.

Monographs:

• Foundations of Ricci flow, University of Science and Technology of China Press, ISBN: 978-7-312-06574-3 (2026). Some Errata.