Welcome to Freid Tong's Homepage

Contact Information

20 Garden Street,

Cambridge, MA 02138

Office: 106

My name is Freid Tong and I am a postdoctoral fellow at Harvard University's Center for Mathematical Sciences and Applications. Here my mentor is Prof. S.T. Yau. I obtained my Ph.D. in mathematics from Columbia University in April 2021, my advisor was Prof. D.H. Phong.

My research interest is in complex geometry, geometric analysis, and nonlinear PDEs.

I'm an organizer of the Geometry and Tacos online conference series. The next one will be in May 2024 on the topic of Hermitian Yang-Mills Connections.

A free-boundary Monge-Ampere equation and applications to complete Calabi-Yau metrics. (with T.C. Collins and S.T. Yau) arXiv
Generalized Monge-Ampere functionals and related variational problems. (with S.T. Yau) arXiv
On the modulus of continuity of solutions to complex Monge-Ampere equations. (with B. Guo, D.H. Phong and C. Wang) arXiv
On L^∞ estimates for Monge-Ampere and Hessian equations on nef classes. (with B. Guo, D.H. Phong and C. Wang) Analysis & PDE. (2024) arXiv
On the Hessian-cscK equations. (with B. Guo and K. Smith) Math. Z. (2023) arXiv
Stability estimates for the complex Monge-Ampere and Hessian equations. (with B. Guo and D.H. Phong) Calculus of Variations and PDEs. (2023). arXiv
A new gradient estimate for the complex Monge-Ampere equation. (with B. Guo and D.H. Phong) Math. Ann. (2022). arXiv
On L^∞ estimates for complex Monge-Ampere equations. (with B. Guo and D.H. Phong) Annals of Math. (2023). arXiv
On the degeneration of asymptotically conical Calabi-Yau metrics. (with T.C. Collins and B. Guo) Math. Ann. (2022). arXiv
A new positivity condition for the curvature of Hermitian manifolds. Math. Z. (2021). arXiv
Longtime existence of Kähler-Ricci flow and holomorphic sectional curvature. (with S. Huang, M.-C. Lee and L.F. Tam) Comm. Anal. Geom. (2023) arXiv
The Kähler-Ricci flow on manifolds with negative holomorphic curvature. arXiv

Instructor for MATH289Y: Topics in Geometric PDEs, Harvard University, Fall 2023
Instructor for Math 1b, Harvard University, Fall 2022
During Summer 2022, I was a research mentor for Introduction to Mathematical Research course at Harvard and I supervised 3 undergraduate student projects.
Instructor for Linear Algebra, Columbia University, Summer 2021
Instructor for Calculus IV, Columbia University, Summer 2020
Instructor for Calculus IV, Columbia University, Summer 2019