大语言模型辅助研究 LLM-Assisted Research
自 2026 年 8 月起，我开始将大语言模型（LLMs）用于科研。模型参与的方式与程度因项目而异。在部分工作中，主要思想和论证由我与合作者提出和完成，模型主要用于探索、核验、技术推导或文字表述；在另一些工作中，模型则更深入地参与数学思想与证明的发现和发展。
在所有工作中，作者均认真审查并核验数学论证，并对最终成果负责。
2026 Scalar curvature bounds and tangent cones for Kähler-Ricci shrinkers
with J. Zhang, arXiv:2610.05643.
2026 On the tangent flows of noncollapsed Ricci flow limit spaces
with B. Wang, arXiv:2610.05204.
此前预印本 Earlier Preprints
2026 Gromov-Hausdorff limits of noncollapsed Kähler-Ricci flows and the geometry of Ricci shrinkers
with J. Zhang, arXiv:2607.25644.
2026 Gromov-Hausdorff convergence of time-slices of singular Ricci flows in dimension three
arXiv:2606.13301.
2026 Strong uniqueness and rectifiability of generalized cylindrical singularities in Ricci flow
with H. Fang, arXiv:2605.17001.
2025 Singular sets in noncollapsed Ricci flow limit spaces
with H. Fang, arXiv:2510.26317.
2025 Strong uniqueness of tangent flows at cylindrical singularities in Ricci flow
with H. Fang, arXiv:2510.20320.
2025 On the structure of noncollapsed Ricci flow limit spaces
with H. Fang, arXiv:2510.12398.
2025 Volume estimates for the singular sets of mean curvature flows
with H. Fang, arXiv:2504.09811.
已发表或接受论文 Publications
待刊 On the rigidity of Ricci shrinkers
with W. Zhang, arXiv:2305.06143. Journal of the European Mathematical Society（已接受，待刊）。
2026 Non-collapsing of Ricci shrinkers with bounded curvature
with C. Dong, Mathematische Annalen, 394, 7 (2026).
2026 On Kähler Ricci shrinker surfaces
with B. Wang, Acta Mathematica, Vol. 236, Issue 1 (2026), pp. 1-50.
2025 Uniqueness of Kähler Ricci shrinkers on toric orbifolds
with W. Zhang, The Journal of Geometric Analysis, 35, 142 (2025).
2024 Heat kernel on Ricci shrinkers (II)
with B. Wang, Acta Mathematica Scientia, 44, 1639-1695 (2024).
2024 Rigidity of the round cylinders in Ricci shrinkers
with B. Wang, Journal of Differential Geometry, Vol. 127, No. 2 (2024), 817-897.
2024 Ancient solutions to the Kähler Ricci flow
Geometry & Topology 28 (2024), no. 7, 3257-3283. 更强结果.
2023 Rigidity of complex projective spaces in Ricci shrinkers
with W. Zhang, Calculus of Variations and Partial Differential Equations 62, 171 (2023).
2023 Ancient solutions to the Ricci flow with isotropic curvature conditions
with J. Cho, Mathematische Annalen, 387, 1009-1041 (2023).
2021 On the geometry of asymptotically flat manifolds
with X. Chen, Geometry & Topology 25 (2021), no. 5, 2469-2572.
2021 On the structure of Ricci shrinkers
with H. Li and B. Wang, Journal of Functional Analysis, Volume 280, Issue 9, 1 May 2021, 108955.
2021 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.
2020 Heat kernel on Ricci shrinkers
with B. Wang, Calculus of Variations and Partial Differential Equations 59, 194 (2020).
2019 The rigidity of Ricci shrinkers of dimension four
with B. Wang, Transactions of the American Mathematical Society 371 (2019), 6949-6972.
2018 Ricci flow on asymptotically Euclidean manifolds
Geometry & Topology 22 (2018), no. 3, 1837-1891.
2014 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.
专著 Monographs
2026 Foundations of Ricci flow
中国科学技术大学出版社，2026 年。ISBN: 978-7-312-06574-3。勘误。
科研项目 Grants
国家自然科学基金委员会青年科学基金项目（B类），主持，2026.1-2028.12。
国家重点研发计划青年科学家项目，主持，2025.12-2030.11。
国家自然科学基金委员会青年科学基金项目（C类），主持，2023.1-2025.12。
中国科学院稳定支持基础研究领域青年团队，参与，2021.6-2026.5。