Laiyuan Gao （or Lai-Yuan Gao, in Chinese 高来源）
Research interest: differential geometry and geometric analysis
Office: Room 208 of the 21st Century Building
我主要研究几何分析，其思想是使用偏微分方程研究微分几何和拓扑学。
近年来感兴趣的课题是平均曲率流、Ricci 流和曲线流，
其中后两者是 Hamilton 和 Perelman 证明 Poincare 猜想的关键技术。
读几何方向研究生的同学，将来会系统学习偏微分方程、拓扑学以及 Riemann 几何。
如果本科阶段没有学过大学微分几何课，需要在研一开学前自学一下。
lygao@jsnu.edu.cn
CV
我本科毕业于淮阴师范学院，毕业论文导师是孙智宏教授。
硕士研究生就读于徐州师范大学（江苏师范大学），导师为张运涛教授。
2011.09 - 2014.06, Tongji University, Ph. D., Majored in Pure Mathematics
(Supervisor is Prof. Shengliang Pan. In my opinion, Prof. Bendong Lou is also my advisor.)
2014.07 - 2016.07, Shanghai University, Postdoc (Advisor is Prof. Gangsong Leng.)
2016.08 - 2020.06, Jiangsu Normal University, Lecturer/Assistant Professor
2019.10 - 2021.01, UC San Diego, Visiting Scholar (Mentor is Prof. Lei Ni.)
2020.07 - present, Jiangsu Normal University, Associate Professor
Scientific Research
1. Selected Papers
[5] Gao, L. Whitney-Graustein homotopy of locally convex curves via a curvature flow, Math. Res. Lett. 30 (2023), no. 4, 1045–1062. （本文对局部凸曲线的情形解决了 Yau 提出的曲率流公开问题。
Paul Bryan's review.pdf）
[4] Gao, L.; Pan, S. Star-shaped centrosymmetric curves under Gage's area-preserving flow. J. Geom. Anal. 33 (2023), no. 11, Article No. 348.（本文尝试解决如下的 folklore conjecture：简单闭星形曲线的 Gage 保面积流全局存在。Vasyl Gorkavyy's review 2.pdf 此问题最新的进展为我们的结果 arXiv:2412.18102）
[3] Gao, L.; Pan, S.; Tsai, D.-Ho On an area-preserving inverse curvature flow of convex closed plane curves, J. Funct. Anal. 280 (2021), no. 8, Paper No. 108931. （本文解决了Kappa^（- alpha）型保面积流的收敛性问题。）
[2] Gao, L.; Zhang, Y. On Yau's problem of evolving one curve to another: convex case. J. Differential Equations, no. 1, 266 (2019), 179–201. （本文对凸曲线的情形解决了 Yau 提出的曲率流公开问题。Vasyl Gorkavyy's review 1.pdf）
[1] Gao, L.; Pan, S. Gage's original normalized CSF can also yield the Grayson theorem. Asian J. Math. 20 (2016), no. 4, 785–794. （本文给出 Gage-Hamilton-Grayson 定理的新证明。）
A list of my papers.txt A list of my papers-2.txt (up to 2025-01-01)
2. Fundation
2019-2021, NSFC-11801230
2015-2016, CPSF-2015M571537
Teaching
1. Recent Courses
2025.02 - 2025.06, Geometry of Submanifolds (研一), Mathematical Modeling (本科生)
2024.09 - 2025.01, Geometic Analysis (研二), Theory of Curvature Flows (研二)
2. Seminars on Geometry （每周日有一整天的讨论）
Year 2024, Hamilton's invention of his Ricci flow notes.pdf
Year 2025, Singularity analysis of curvature flows
Social Service
1. AMS Reviewer for Rev. Mat. Iberoam..pdf Trans. Amer. Math. Soc..pdf J. Reine Angew. Math..pdf ...
2. Referee for many journals...
Links to some mathematicians