1. 非负数量曲率流形类的紧性与正则性问题；

2. Einstein度量的稳定性问题.

2011年9月至2016年6月 University of California, Santa Barbara, 获数学博士学位

2008年9月至2011年6月 中国科学技术大学, 获理学硕士学位

2004年9月至2008年7月 中国科学技术大学, 获理学学士学位

发表论文

1.(with X. Dai and Y. Sun) Positive mass theorem for asymptotically flat spin manifolds with isolated conical singularities, Transactions of the American Mathematical Society, 378 (4), 2617-2646, (2025).

2.(with X. Dai and Y. Sun) Positive mass theorem for asymptotically flat manifolds with isolated conical singularities, Science China Mathematics, Vol. 68, No. 7, 1671-1686, (2025).

3.(with Y. Sun) Gap phenomenon for scalar curvature, Journal ofGeometric Analysis, Volume 35, article number 275, (2025).

4.(with W. Tian) Compactness of sequences of warped product circles over spheres with nonnegative scalar curvature, Mathematische Annalen, 390, no. 2, 2767-2823, (2024).

5.(with X. Dai) Perelman's functionals on manifolds with non-isolated conical singularities, Calculus of Variations and Partial Differential Equations, Volume 63, article number 233, 51 pages, (2024).

6.(with C. Sormani and W. Tian) An extreme limit with nonnegative scalar curvature, Nonlinear Analysis, 239, Paper No. 113427, 24 pp, (2024).

7.(with M. Wang) Instability of some Riemannian manifolds with real Killing spinors, Communications in Analysis and Geometry, 30(8), 1895-1931, (2022).

8.(with U. Semmelmann and M. Wang) Linear Instability of Sasaki Einstein and nearly parallel G2 manifolds, International Journal of Mathematics, 33(6), Paper No. 2250042, 17 pages, (2022).

9.(with F. He) Regularity estimates for the gradient flow of a spinorial energy functional, Mathematical Research Letters, 28(4), 1125-1173, (2021).

10.(with M. Wang) Stability of Einstein metrics on fiber bundles, Journal of Geometric Analysis, 31, 490-515, (2021).

11.(with X. Dai) Perelman's W-functional on manifolds with conical singularities, Mathematical Research Letters, 27(3), 665-685, (2020).

12.(with U. Semmelmann and M. Wang) On the linear stability of nearly Kaehler 6-manifolds, Annals of Global Analysis and Geometry, 57(1), 15-22, (2020).

13.(with J. Park and W. Tian) A compactness theorem for rotationally symmetric Riemannian manifolds with positive scalar curvature, Pure Applied Mathematics Quarterly, 14(3-4), 529-561, (2018).

14.(with X. Dai) Perelman's lambda-functional on manifolds with conical singularities, Journal of Geometric Analysis, 28(4), 3657-3689, (2018).

15.Stability of Riemannian manifolds with Killing spinors, International Journal of Mathematics, 28(1), 1750005, 19 pages, (2017).

预印本

16.(with B. Allen and W. Tian) On the scalar curvature compactness conjecture in the conformal case, Accepted by Calculus of Variation and Partial Differential Equations, (2025), arXiv:2406.03988.

17.(with X. Dai, L. Wang and G. Wei) Singular metrics with nonnegative scalar curvature and RCD, arXiv:2412.09185.

18.(with X. Dai, Y. Sun) Positive scalar curvature and isolated conical singularity, arXiv:2412.02941.

本科教学：

2025.02 – 2025.07, 数学分析(荣)下

2024.02 – 2024.07, 数学分析(荣)下

2023.09 – 2024.01, 数学分析(下)；数学分析(下)习题课

2022.09 – 2023.01, 数学分析(下)；数学分析(下)习题课

2021.09 – 2022.01, 数学分析(下)；数学分析(下)习题课

2020.09 – 2021.01, 解析几何(强基班)

研究生指导：

指导毕业了3名硕士研究生，现指导在读直博生2名.