I'm interested in Complex Geometry, Complex Algebraic Geometry.
Some specific topics are: Complex Monge-Ampère equations, Kahler Ricci flow, Analytic Minimal Model Program.
My papers on ArXiv
| Publications |
- Regularizing properties of Complex Monge-Ampère flows, J. Funct. Anal. 272 (2017), no. 5, 2058–2091.
- Regularizing properties of Complex Monge-Ampère flows II: Hermitian manifolds, Math. Ann. 372 (2018), Issue 1–2, pp 699–741 (arXiv )
- (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
- (with Duong H. Phong) Fully non-linear parabolic equations on compact Hermitian manifolds, accepted in Annales Scientifiques de l’ENS, arXiv:1711.10697
- Convergence of the weak Kähler-Ricci Flow on manifolds of general type, accepted in IMRN, DOI: 10.1093/imrn/rnz256 , arXiv:1905.01276
- (with H-S Do and Giang Le) Viscosity solutions to parabolic complex Monge-Ampère equations, accepted in Calculus of Variations and PDEs, 59, 45 (2020), arXiv:1905.11818
| Preprints and In preparation |
• (with S. Puechmorel) Convergence of the Hesse-Koszul flow on compact Hessian manifolds, arXiv:2001.02940
• (with H. C. Lu et T. T. Phung) Stability and Hölder regularity of solutions to complex Monge-Ampère equations on compact Hermitian manifolds, arXiv:2003.08417
| Invited Talks |
• Jan, 2018 Informal Geometry Workshop in ”Paradiso”, Cogne, Italy.
• Apr, 2017 Regularizing properties of complex Monge-Ampere flows
Informal Complex Geometry and PDE Seminar, Columbia University, New York.
• Nov, 2016 The Kahler-Ricci flow on complex surfaces, Complex geometry seminar, IMT, Toulouse.
• Oct, 2016 The Kahler-Ricci flow and Minimal model program, Rencontres doctorales Lebesgue, Angers.
• Jun, 2016 Parabolic Monge-Ampere equations on Kahler manifolds, Journee de Recherche, Paris.
• Mar, 2016 Multiplier ideal sheaves with weights of Lelong number one , Complex geometry seminar, IMT.
• Feb, 2016 Kleiman’s and Nakai-Moishezon’s ampleness criteria, Algebraic geometry seminar, IMT, Toulouse.