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Research

My research interests are in differential geometry, geometry analysis, mathematical physics and related areas.

My publications can be found on arXiv, Google Scholar, MathSciNet, INSPIRE.

 

  1. On nilpotent Jordan structures.
  2. The geometry of three-forms on symplectic six-manifolds.
  3. Remarks on generalized Calabi-Gray manifolds. To appear in Int. J. Math.
  4. (With D.H. Phong, S. Picard and X.-W. Zhang). Stability of the Type IIA flow and its applications in symplectic geometry. To appear in Comm. Anal. Geom.
  5. (With D.H. Phong). Symplectic geometric flows. Pure Appl. Math. Q. 19 (2023), No. 4, 1853-1871. Published Version
  6. (With D.H. Phong, S. Picard and X.-W. Zhang). Bochner-Kodaira formulas and the Type IIA flow. J. Geom. Anal. 33 (2023), No. 2, 48. Published Version. MR4523515.
  7. (With D.H. Phong, S. Picard and X.-W. Zhang). Geometric flows for the Type IIA string. Camb. J. Math. 9 (2021), No. 3, 693-807. Published Version. MR4400736.
  8. (With D.H. Phong, S. Picard and X.-W. Zhang). Estimates for a geometric flow for the Type IIB string. Math. Ann. 382 (2022), No. 3-4, 1935-1955. Published Version. MR4403240.
  9. (With D.H. Phong). Unification of the Kähler-Ricci and Anomaly flows. In Differential Geometry, Calabi-Yau Theory, and General Relativity, 89-104 (2018), Vol. 23 of Surveys in Differential Geometry, International Press. Published Version. MR4451825.
  10. (With S. Picard). Anomaly flow and T-duality. Pure Appl. Math. Q. 17 (2021) No. 3, 1083-1112. Published Version. MR4278960.
  11. (With B. Guo and D.H. Phong). On convergence criteria for the coupled flow of Li-Yuan-Zhang. Math. Z. 292 (2019) No. 1-2, 473-497. Published Version. MR3968911.
  12. Generalized Calabi-Gray geometry and heterotic superstrings. In Proceedings of the International Consortium of Chinese Mathematicians, 2017, 261-282 (2020), International Press. Published Version. MR4251114.
  13. (With B. Guo and D.H. Phong). Parabolic dimensional reductions of 11D supergravity. Anal. PDE 14 (2021), No. 5, 1333–1361. Published Version. MR4307211.
  14. (With B. Guo and D.H. Phong). A geometric construction of solutions to 11D supergravity. Comm. Math. Phys. 369 (2019) No. 2, 811-836. Published Version. MR3962009.
  15. (With Z.-J. Huang and S. Picard). The Anomaly flow over Riemann surfaces. Int. Math. Res. Not. 2021 (2021), No. 3, 2134-2165. Published Version. MR4206607.
  16. (With Z.-J. Huang). An estimate of the first eigenvalue of a Schrödinger operator on closed surfaces. Proc. Amer. Math. Soc. 146 (2018) No. 4, 1599-1602. Published Version. MR3754344.
  17. (With Z.-J. Huang and S. Picard). A construction of infinitely many solutions to the Strominger system. J. Differential Geom. 117 (2021) No. 1, 23-39. Published Version. MR4195751.
  18. Some torsional local models of heterotic strings. Comm. Anal. Geom. 25 (2017) No. 5, 941-968. Published Version. MR3733796.
  19. A construction of non-Kähler Calabi-Yau manifolds and new solutions to the Strominger system. Adv. Math. 302 (2016), 529-550. Published Version. MR3545938.
  20. Stable forms, vector cross products and their applications in geometry. Preprint.
  21. (with S.-T. Yau). Invariant solutions to the Strominger system on complex Lie groups and their quotients. Comm. Math. Phys. 338 (2015) No. 3, 1183-1195. Published Version. MR3355812.
  22. (with K. Cordwell and K. Zhou). On lower central series quotients of finitely generated algebras over Z. J. Algebra 423 (2015), 559-572. Published Version. MR3283731.
  23. (With J. Zhang). Information Geometry with (Para-)Kähler Structures. In Information Geometry and Its Applications: IGAIA IV Liblice, Czech Republic, June 2016, 297-321 (2018), Springer. Published Version. MR3876122.
  24. (With J. Zhang). Interaction of Codazzi couplings with (para-)Kähler geometry. Results Math. 72 (2017) No. 4, 2037-2056.
    Published Version. MR3735541.
  25. My Thesis. MR3593383.

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