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Research interests

  1. Pluripotential theory.
  2. Complex geometry and dynamics.

Preprints

  1. Big and nef cohomology classes on compact Kaehler spaces, arXiv:2609.07489 , 2026.
  2. Positivity of Smooth Currents on Singular Spaces (with Duc-Thai Do), arXiv:2609.04335 , 2026.
  3. Quantitative hyperbolicity for complex manifolds via numerical invariants (with Tien-Cuong Dinh and Duc-Bao Nguyen), arXiv:2607.07054 , 2026.
  4. Singularity of non-pluripolar cohomology classes (with Duc-Bao Nguyen and Shuang Su), arxiv:2508.14669 , 2025.
  5. A survey on asymptotic equilibrium distribution of zeros of random holomorphic sections (with George Marinescu), arXiv:2504.15083 , 2025.
  6. Uniform diameter estimates for Kähler metrics in big cohomology classes (with Duc-Bao Nguyen), arXiv:2410.18532 , 2024.
  7. Log continuity of solutions of complex Monge-Ampère equations (with Hoang-Son Do), arXiv:2312.04128 , 2023.

Publications

  1. Non-collapsing volume estimate for local Kähler metrics in big cohomology classes (with Thai Duong Do and Duc-Bao Nguyen), arXiv:2502.16136 , Math. Z. 312 (2026), Paper No. 113.
  2. Uniform diameter and non-collapsing estimates for Kähler metrics , arXiv:2405.14680 , J. Geom. Anal. 36 (2026), Paper No. 75.
  3. Kähler–Einstein metrics on quasi-projective manifolds (with Quang-Tuan Dang), arXiv:2309.03858 , Math. Ann. 392 (2025), 4071–4103.
  4. Quantitative stability for the complex Monge-Ampère equations II (with Hoang-Son Do), arXiv:2209.00248 , Calc. Var. Partial Differential Equations 64 (2025), Paper No. 269.
  5. Volumes of components of Lelong upper level sets II (with Shuang Su), arXiv:2404.14058 , Math. Ann. 391 (2025), 6451–6465.
  6. Equidistribution for non-pluripolar currents on compact Kähler manifolds (with Taeyong Ahn), arXiv:2309.12099 , Anal. Math. Phys. 14 (2024), no. 6, Paper No. 115
  7. Quantitative stability for complex Monge-Ampère equations, I (with Hoang-Son Do), arXiv:2405.17491 , Anal. PDE 18 (2025), no. 5, 1271–1308.
  8. Continuity of functions in complex Sobolev spaces , arXiv:2312.01635 , Pure Appl. Math. Q. 20 (2024), no. 6, 2769–2780.
  9. Derivative of volumes of big cohomology classes , arXiv:2307.15909 , Indiana Univ. Math. J. 74 (2025), no. 6, 1531–1560.
  10. Lebesgue points of functions in complex Sobolev spaces (with Gabriel Vigny), arXiv:2306.12332 , 2023, Internat. J. Math. 35 (2024), no. 5, Paper No. 2450014, 22 pp.
  11. Bergman kernel functions associated to measures supported on totally real submanifolds (with George Marinescu), arXiv:2210.11031 , J. reine angew. Math. 810 (2024), 217-251.
  12. Volume of components of Lelong upper level sets (with Duc-Thai Do), arXiv:2301.05960 , J. Geom. Anal. 33 (2023), no. 9, Paper No. 303, 14 pp. in a volume in Memoriam of Nessim Sibony.
  13. Higher Lelong numbers versus full Monge-Ampère mass (with Duc-Thai Do), arXiv:2104.05434 , J. Differential Geom. 128 (2024), no. 2, 903-927.
  14. Complex Monge-Ampere equations with solutions in finite energy classes (with Duc-Thai Do), Math. Res. Lett. 29 (2022), no. 6, 1659-1683, arXiv:2010.08619.
  15. Lelong numbers of currents of full mass intersection , Amer. J. Math. 145 (2023), no. 2, 647-665, arXiv:2008.09219.
  16. Moser-Trudinger inequalities and complex Monge-Ampere equations (with Tien-Cuong Dinh and George Marinescu), Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 24 (2023), no. 2, 927-954, arXiv:2006.07979.
  17. Convexity of the class of currents with finite relative energy , Ann. Polon. Math. 128 (2022), no. 3, 275-288, arXiv:2005.13241.
  18. Relative non-pluripolar products of currents , Ann. Global Anal. Geom. 60 (2021), no. 2, 269-311, arXiv:2004.11111.
  19. Intersection of (1,1)-currents and the domain of definition of the Monge-Ampere operator (with Dinh Tuan Huynh and Lucas Kaufmann), Indiana Univ. Math. J. 72 (2023), no. 1, 239-261, arXiv:2003.12501.
  20. Exotic periodic points , Commun. Contemp. Math. 24 (2022), no. 5, Paper No. 2150029, 15 pp, (part of arXiv:1902.00666).
  21. Density currents and relative non-pluripolar products , Bull. Lond. Math. Soc. 53 (2021), no. 2, 548-559, arXiv:2006.16803.
  22. On the set of divisors with zero geometric defects (with Dinh Tuan Huynh), J. reine angew. Math. 771 (2021), 193-213, arXiv:1907.08740.
  23. Densities of currents on non-Kahler manifolds , Int. Math. Res. Not. IMRN (2021), no. 17, 13282-13304 (part of arXiv:1902.00666).
  24. Equibirium measures for meromorphic self-maps on non-Kahler manifolds , Trans. Amer. Math. Soc. 373 (2020), no. 3, 2229-2250, arXiv:1901.04775.
  25. Locally pluripolar sets are pluripolar , Internat. J. Math. 30 (2019), no. 13, 1950029, 13 pp arXiv:1812.00465.
  26. Algebraic flows in commutative complex Lie groups (with Tien-Cuong Dinh), Comment. Math. Helv. 95 (2020), no. 3, 421-460, arXiv:1811.09823.
  27. Densities and intersection of (1,1)-currents (with Lucas Kaufmann), arXiv:1804.09980, J. Funct. Anal. 277 (2019), no. 2, 392-417.
  28. Super-potentials, densities of currents and number of periodic points for holomorphic maps (with Tien-Cuong Dinh and Viet-Anh Nguyen), Adv. Math. 331 (2018), 874-907, arXiv:1710.01473.
  29. Families of Monge-Ampere measures with Holder continuous potentials , Proc. Amer. Math. Soc. 146 (2018), no. 10, 4275-4282, arXiv:1708.09595, 2017.
  30. Large deviation theorem for random covariance matrices (with Tien-Cuong Dinh), arXiv:1707.07174, Michigan Math. J. 68 (2019), no. 3, 597-620.
  31. Entire holomorphic curves into projective spaces intersecting a generic hypersurface of high degree (with Dinh Tuan Huynh and Song-Yan Xie), arXiv:1704.03358, Ann. Inst. Fourier (Grenoble) 69 (2019), no. 2, 653-671.
  32. Complex Monge-Ampere equation for measures supported on real submanifolds , Math. Ann. 372 (2018), no. 1-2, 321-367, arXiv:1608.02794.
  33. Equidistribution rate for Fekete points on some real manifolds , Amer. J. Math. 140 (2018), no. 5, 1311-1355, arXiv: 1512.08262.
  34. Intersection of positive closed currents of higher bi-degree , Michigan Math. J. 65 (2016), no. 4, 863-872, arXiv:1507.05464.
  35. Asymptotic number of scattering resonances for generic Schrodinger operators (with Tien-Cuong Dinh), Comm. Math. Phys. 326 (2014), no. 1, 185-208, arXiv:1207.4273.
  36. Holomorphic mappings into compact complex manifolds (with Duc-Thai Do), Houston J. Math. 43 (2017), no. 3, 725-762, arXiv:1301.6994.

Miscellaneous notes

  1. Loss of mass of non-pluripolar products, arXiv:2101.05483 , 2020, preprint.
  2. Densities of currents and complex dynamics, arXiv:1902.00666 , 2019 (this version is not intended to submit, parts of it will be submitted separately).