Research interests


  1. Pluripotential theory.


  2. Complex dynamics and foliations.


  3. Complex geometry.

Preprints


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


  2. Higher Lelong numbers versus full Monge-Ampθre mass (with Do Duc Thai), arXiv:2104.05434, 2021.


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


  4. Complex Monge-Ampere equations with solutions in finite energy classes (with Do Duc Thai), arxiv:2010.08619 , 20 pages, 2020, to appear in Math. Res. Lett. .


  5. Lelong numbers of currents of full mass intersection, arxiv:2008.09219 , 17 pages, 2020, to appear in Amer. J. Math..


  6. Moser-Trudinger inequalities and complex Monge-Ampere equations (with Tien-Cuong Dinh and George Marinescu), arxiv:2006.07979, 22 pages, 2020, to appear in Ann. Sc. Norm. Super. Pisa Cl. Sci. (5).


  7. Convexity of the class of currents with finite relative energy, arxiv:2005.13241, 2020, to appear in Annales Polonici Mathematici.


  8. Relative non-pluripolar products of currents, arxiv:2004.11111, 41 pages, 2020, to appear in Ann. Global Anal. Geom..


  9. Intersection of (1,1)-currents and the domain of definition of the Monge-Ampere operator (with Dinh Tuan Huynh and Lucas Kaufmann), arxiv:2003.12501, 13 pages, 2020, to appear in Indiana Univ. Math. J..


  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. Exotic periodic points, preprint, 2019 (part of arxiv:1902.00666), to appear in Commun. Contemp. Math..


  2. Density currents and relative non-pluripolar products, arxiv:2006.16803, 12 pages, 2020, to appear in Bull. London. Math. Soc.


  3. On the set of divisors with zero geometric defects (with Dinh Tuan Huynh), arxiv:1907.08740, 19 pages, 2019, to appear in Crelle's journal.


  4. Densities of currents on non-Kahler manifolds, final version (part of arxiv:1902.00666), 17 pages, 2019, to appear in Int. Math. Res. Not. IMRN.


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


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


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


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


  9. 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.


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


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


  12. 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.


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


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


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


  16. 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.


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