Research

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

Some specific topics are: Kähler geometry, geometric flows, complex Monge-Ampère equations, constant scalar curvature Kahler (cscK) metrics, Φ^4_3 model. 

I'm also interested in Artificial intelligence and application of AI in healthcare. See below for related publications.

I defended my HDR in March 2025

Preprints:

• On Käher-Einstein Currents, arXiv:2502.09825 (2025),  with Y. Chen, S-K. Chiu, M. Hallgren, G. Székelyhidi, and F. Tong

• Weighted cscK metrics on Kähler varieties, arXiv:2412.07968 (2024), with C-M. Pan

• An iterative construction of complete Kähler-Einstein metrics, arXiv:2410.12599 (2024), with Q-T. Dang

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

•  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), with I. Bailleul, N.V. Dang, L. Ferdinand

Articles:

• Kähler families of Green's functions, Journal de l’École polytechnique-Mathématiques, Volume 12 (2025), pp. 319-339, arXiv, (with V. Guedj)

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

• Monge-Ampère equations on compact Hessian manifolds, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)   25 (2024), no. 1, 291–310. arXiv, (with V. Guedj)

• 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 S. Puechmorel)

• 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, (with H. C.  Lu et T. T. Phung) 

• 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

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

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

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

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

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

Artificial intelligence:

• United States Patent : Compute system with acne diagnostic mechanism and method of operation thereof, Patent No. US12190515B2 (2025), avec T-D. Nguyen, H. Nguyen, L. Gazeau et D. V. Han. 

• (with others) AcneAI : A new acne severity assessment method using digital images and deep learning, MICCAI 2024, 27th International Conference on Medical Image Computing and Computer Assisted Intervention

• (with others) A Fast and Simple Modification of Newton’s Method Avoiding Saddle Points, Journal of Optimization Theory and Applications (2023)

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

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:

• Canonical Kähler metrics and the Φ43 quantum field theory, HDR thesis, defended on March 5, 2025 at IMJ-PRG.

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