Song, Chong / 宋翀

(Last updated in June. 2024)

诚招研究生与博士后，欢迎对几何分析方向感兴趣的同学与我联系！

Research Interests

Geometric analysis, including:

Blow-up analysis of Harmonic maps and Yang-Mills-Higgs fields;

Hamiltonian Geometric flows, especially Skew mean curvature flow, Schrodinger map flow and their geometric solitons.

Research papers:

Preprints:

19. "Isolated singularities of 3-dimensional Yang-Mills-Higgs fields" (with Bo Chen), arXiv:2406.16276.

18. "Finite-time singularities of 2D Landau-Lifshitz flow for almost-holomorphic maps" (with Ze Li), preprint 2023.

Published papers:

16. "Harmonic map flow for almost-holomorphic maps " (with Alex Waldron), to appear in J. Diff. Geom. arXiv:2009.07242.

15. "Harmonic maps with free boundary from degenerating bordered Riemann surfaces"(with Lei Liu, Miaomiao Zhu), J. Geom. Anal. 32(2), Paper No. 49, 21pp(2022).

14. "Local existence and uniqueness of skew mean curvature flow", J. Reine Angew. Math. No. 776, 1–26 (2021).

13. "Isolated singularities of Yang-Mills-Higgs fields on surfaces"(with Bo Chen), Intern. Math. Res. Not. Vol. 2021, No. 1, 551-581 (2020).

12. "The boundary value problem for Yang--Mills--Higgs fields"(with Wanjun Ai, Miaomiao Zhu), Calc. Var. PDE. 58(4), paper no. 157 (2019).
11. "Hessian estimates for convex solutions to quadratic Hessian equation"(with Matt McGonagle, Yu Yuan), Ann. I. H. Poincaré - AN, 36(2), 451-454 (2019).
10.“Skew Mean Curvature Flow”(with Jun Sun), Commun. Contemp. Math. Vol. 21, No. 01, 1750090 (2019).
9.“Uniqueness of Schrodinger flow on manifolds"(with Youde Wang), Comm. Anal. Geom. 26, no. 1, 217–235(2018).
8. "Gauss map of Skew mean curvature flow", Proc. Amer. Math. Soc. 145, no. 11, 4963–4970(2017).
7.“Heat flow of Yang-Mills-Higgs functional in dimension two”(with Changyou Wang), J. Funct. Anal. 272, No. 11, 4709–4751 (2017).
6.“Convergence of Yang-Mills-Higgs fields”, Math. Ann. Vol. 366, No. 1, 167-217(2016).
5.“Geometric soliton of Hamiltonian flow on manifolds”(with Xiaowei Sun, Youde Wang),Journal of Mathematical Physics, Vol. 54, No. 12,121505(2013).
4.“The Cauchy problem of generalized Landau-Lifshitz equation into Sn”(with Jie Yu),Science in China Series A, Vol. 56, No. 2, 283-300(2013).
3.“The KdV-Airy curve and the Schrodinger-Airy curve”, Proc. Amer. Math. Soc., 140, 635-644(2012).
2.“Schrodinger solitons from Lorentzian manifolds”(with Youde Wang),Acta Mathematica Sinica, English Series”, Vol. 27, No. 8, 1455-1476(2011).
1.“Critical points of Yang-Mills-Higgs functional”,Commun. Contemp. Math., Vol. 13, No. 3, 463–486(2011)

Teaching

Lecture notes for Differentiable Manifolds (2020) pdf

《自然科学中的数学》讲义(2020)   MNS2020Calculus1.pdf   MNS2020Calculus2.pdf

 教学比赛ppt (2015)

Honors

2021年 厦门市优秀教师

2021年 主持福建省本科高校教学改革项目

2020年 教育部“长江学者奖励计划”青年学者项目

2018年 厦门大学“翻转课堂”教学比赛一等奖

2015年 厦门大学第九届青年教师教学技能大赛特等奖

2015年 全国高校数学微课程教学设计竞赛华东赛区一等奖

Research Grants

9. 2024, “关于带联络的薛定谔流的适定性的研究”, 数学天元基金项目，no. 12326359;

8. 2024-2027, “耦合度量发展方程的映射流及其爆破分析”, NSFC面上项目，no. 12371061;

7. 2021-2024, “几何流与爆破分析”，福建省自然科学基金杰青项目，no. 2021J06005；

6. 2020-2023, "具有物理背景的两类几何发展方程研究", NSFC 面上项目, no. 11971400;

5. 2017-2019, "斜平均曲率流". Fundamental Research Funds for the Central University，no. 20720170009;

4. 2014-2016, "扭曲调和映射的若干问题及其应用",  Natural Science Foundation of Fujian Province of China, no. 2014J01023;

3.2013-2015, "KdV曲线与KdV孤立子", NSFC 青年项目, no. 11201387;

2.2013-2015, "一类几何偏微分方程的爆破分析". Specialized Research Fund for the Doctoral Program of Higher Education(SRFDP), no. 20120121120022;

1. 2011, "扭曲调和映射模空间的紧化", China Postdoctoral Science Foundation，no. 201110490223.

Working Experiences

2020.8--            Professor,

2013.8--2020.7   Associate Professor,

2011.6--2013.7   Assistant Professor,

School of Mathematical Sciences, Xiamen Univ., China

2009.7--2011.6   Postdoc , Advisor: Tian, Gang

School of Mathematical Sciences, Peking Univ., China

Visiting positons

University of Kentucky(hosted by Wang, Changyou), March 1–April 25, 2013  AMS Fan Fund China Exchange Program

University of British Coulumbia(hosted by Chen, Jingyi), June 1-August 30, 2015

University of Washington(hosted by Yuan, Yu), September 7, 2015-September 7, 2016 CSC visiting scholar

Higher Education

2004.9--2009.7  Ph.D. , Academy of Mathematics, Chinese Academy of Sciences, China   Advisor: Wang, Youde and Tian, Gang

2000.9--2004.7  B.S., School of Mathematics, Wuhan University, China

Links: MathReview / Orcid / ResearchGate / arXiv