Research interests


  1. Pluripotential theory.


  2. Complex dynamics and foliations.


  3. Complex geometry.

Preprints


  1. Log continuity of solutions of complex Monge-Ampère equations (with Hoang-Son Do), arxiv:2312.04128, 2023.


  2. Continuity of functions in complex Sobolev spaces, arxiv:2312.01635, 2023.


  3. Equidistribution for non-pluripolar currents on compact Kähler manifolds (with Taeyong Ahn), arxiv:2309.12099, 2023.


  4. Kähler--Einstein metrics on quasi-projective manifolds (with Quang-Tuan Dang), arXiv.2309.03858, 2023.


  5. Derivative of volumes of big cohomology classes, arXiv:2307.15909, 2023.


  6. Lebesgue points of functions in complex Sobolev spaces (with Gabriel Vigny), arXiv:2306.12332, 2023, to appear in International Journal of Mathematics.


  7. Bergman kernel functions associated to measures supported on totally real submanifolds (with George Marinescu), arXiv:2210.11031 , 2022, to appear in Crelle's journal.


  8. Quantitative stability for the complex Monge-Ampere equations (with Hoang-Son Do), arXiv:2209.00248, 2022.


  9. Loss of mass of non-pluripolar products, arXiv:2101.05483 , 19 pages, 2020, submitted.


  10. Densities of currents and complex dynamics, arxiv:1902.00666, 32 pages, 2019 (this version is not intended to submit, parts of it will be submitted separately).

Publications


  1. Volume of components of Lelong upper level sets (with Do Duc Thai), arXiv:2301.05960 , 2023, to appear in JGEA in a volume in Memoriam of Nessim Sibony.


  2. Higher Lelong numbers versus full Monge-Ampère mass (with Do Duc Thai), arXiv:2104.05434, 2021, to appear in Journal of Differential Geometry.


  3. Complex Monge-Ampere equations with solutions in finite energy classes (with Do Duc Thai), Math. Res. Lett. 29 (2022), no. 6, 1659–1683, arxiv:2010.08619.


  4. Lelong numbers of currents of full mass intersection, Amer. J. Math. 145 (2023), no. 2, 647–665, arxiv:2008.09219.


  5. 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.


  6. Convexity of the class of currents with finite relative energy, Ann. Polon. Math. 128 (2022), no. 3, 275–288, arxiv:2005.13241.


  7. Relative non-pluripolar products of currents, Ann. Global Anal. Geom. 60 (2021), no. 2, 269–311, arxiv:2004.11111.


  8. 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.


  9. Exotic periodic points, Commun. Contemp. Math. 24 (2022), no. 5, Paper No. 2150029, 15 pp, (part of arxiv:1902.00666).


  10. Density currents and relative non-pluripolar products, Bull. Lond. Math. Soc. 53 (2021), no. 2, 548–559, arxiv:2006.16803.


  11. On the set of divisors with zero geometric defects (with Dinh Tuan Huynh), J. Reine Angew. Math. 771 (2021), 193–213, arxiv:1907.08740.


  12. Densities of currents on non-Kahler manifolds, Int. Math. Res. Not. IMRN (2021), no. 17, 13282–13304 (part of arxiv:1902.00666).


  13. Equibirium measures for meromorphic self-maps on non-Kahler manifolds, Trans. Amer. Math. Soc. 373 (2020), no. 3, 2229–2250, arxiv:1901.04775.


  14. Locally pluripolar sets are pluripolar, Internat. J. Math. 30 (2019), no. 13, 1950029, 13 pp arxiv:1812.00465.


  15. Algebraic flows in commutative complex Lie groups (with Tien-Cuong Dinh), Comment. Math. Helv. 95 (2020), no. 3, 421–460, arxiv:1811.09823.


  16. Densities and intersection of (1,1)-currents (with Lucas Kaufmann), arxiv:1804.09980, J. Funct. Anal. 277 (2019), no. 2, 392–417.


  17. Super-potentials, densities of currents and number of periodic points for holomorphic map (with Tien-Cuong Dinh and Viet-Anh Nguyen), Adv. Math. 331 (2018), 874–907, arxiv:1710.01473.


  18. Families of Monge-Ampere measures with Holder continuous potentials, Proc. Amer. Math. Soc. 146 (2018), no. 10, 4275–4282, arxiv:1708.09595, 2017.


  19. Large deviation theorem for random covariance matrices (with Tien-Cuong Dinh), arxiv:1707.07174, Michigan Math. J. 68 (2019), no. 3, 597–620.


  20. 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.


  21. Complex Monge-Ampepre equation for measures supported on real submanifolds, Math. Ann. 372 (2018), no. 1-2, 321–367, arxiv:1608.02794.


  22. Equidistribution rate for Fekete points on some real manifolds, Amer. J. Math. 140 (2018), no. 5, 1311–1355, arxiv: 1512.08262.


  23. Intersection of positive closed currents of higher bidegree, Michigan Math. J. 65 (2016), no. 4, 863–872, arxiv:1507.05464.


  24. 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.


  25. Holomorphic mappings into compact complex manifolds (with Do Duc Thai), Houston J. Math. 43 (2017), no. 3, 725–762, arxiv:1301.6994.