Song, Chong
(Last updated in June. 2024)
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
Lecture notes for “Mathematics in Natural Sciences”(2020) pdf
Slides for teach competition (2015)
Research Grants
9. 2024, Tianyuan Mathematics Foundation，no. 12326359;
8. 2024-2027, NSFC，no. 12371061;
7. 2021-2024, Natural Science Foundation of Fujian Province of China，no. 2021J06005；
6. 2020-2023, NSFC, no. 11971400;
5. 2017-2019, Fundamental Research Funds for the Central University，no. 20720170009;
4. 2014-2016, Natural Science Foundation of Fujian Province of China, no. 2014J01023;
3.2013-2015, NSFC, no. 11201387;
2.2013-2015, Specialized Research Fund for the Doctoral Program of Higher Education(SRFDP), no. 20120121120022;
1. 2011, 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 positions
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
