Research

I'm interested in Geometric Analysis, Complex Geometry, nonlinear PDEs, and recently Mathematical Physics.

Some specific topics are: Monge-Ampère equation, Fully Nonlinear PDEs, constant scalar curvature Kähler metric, Kähler-Ricci flow,  

Preprints:

• (with V. Guedj) Kähler families of Green's functions, arXiv:2405.17232 (2024)

• (with C-M. Pan and A. Trusiani) Singular cscK metrics on smoothable varieties, arXiv:2312.13653 (2023) 

• (with I. Bailleul, N.V. Dang, L. Ferdinand)  Φ^4_3 measures on compact Riemannian 3-manifolds, arXiv:2304.10185 (2023)

• (with I. Bailleul, N.V. Dang, L. Ferdinand) Global harmonic analysis for Φ^4_3 on closed Riemannian manifolds, arXiv:2306.07757  (2023) 

Articles:

• Degenerate J-flow on compact Kähler manifolds, Math. Z. 303, 97 (2023). (arXiv)

• (with V. Guedj) Monge-Ampère equations on compact Hessian manifolds, arXiv:2106.14740, to appear in  Ann. Sc. Norm. Super. Pisa Cl. Sci. 

• (with S. Puechmorel) Convergence of the Hesse-Koszul flow on compact Hessian manifolds, Ann. Inst. H. Poincaré Anal. Non Linéaire 40 (2023), no. 6, pp. 1385–1414

• (with H. C.  Lu et T. T. Phung)  Stability and Hölder regularity of solutions to complex Monge-Ampère equations on compact Hermitian manifolds, Annales de l'Institut Fourier 71 (2021), no. 5, 2019–2045, arXiv:2003.08417 

• Convergence of the weak Kähler-Ricci Flow on manifolds of general type, Int. Math. Res. Not. 2021, No. 8, 6373–6404,  arXiv:1905.01276, See here a revised version with a detailed proof of Theorem 4.3

• (with Duong H. Phong) Fully non-linear parabolic equations on compact Hermitian manifolds, Ann. Scient. Éc. Norm. Sup. 4e série, t.54, 2021, p.793-829 , (arXiv)

• (with H. S. Do, G. Le) Viscosity solutions to parabolic complex Monge-Ampère equations,  Calculus of Variations and PDEs,  59, 45 (2020), arXiv:1905.11818  

• (with S. Dinew and H.S Do) A viscosity approach to the Dirichlet problem for degenerate complex Hessian type equations,  Analysis & PDE, 12 (2019), No. 2, arXiv:1712.08572

• Regularizing properties of Complex Monge-Ampère flows II: Hermitian manifolds, Math. Ann. 372 (2018), Issue 1–2, pp 699–741  arXiv:1701.04023

• Regularizing properties of Complex Monge-Ampère flows, J. Funct. Anal.  272 (2017), no. 5, 2058–2091  arXiv:1604.06261

Seminars and Groupe de Travail:

• GdT: Yang-Mills, 2024

• Minicours: CFT & Yang-Mills (26-28 Sep. 2023)

• GdT  Metric SYZ conjecture and NA geometry

• Geometry and TACoS

Others:

• Flots de Monge-Ampère complexes sur les variétés hermitiennes compactes, PhD thesis:  supervised by Vincent Guedj and defended on June 29, 2018

• A Fast and Simple Modification of Newton’s Method Avoiding Saddle Points, Journal of Optimization Theory and Applications (2023), with T. T. Tuyen, H. T. Nguyen, T. H. Nguyen, H. P. Nguyen and M. Helmy.

• (with many others) Epidemic Dynamics via Wavelet Theory and Machine Learning with Applications to Covid-19, Biology 2020, 9(12), 477