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Reseach

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.