Welcome to Freid Tong's Homepage

Contact Information

Department of Mathematics

University of Toronto

40 St. George St.

Toronto, Ontario, Canada

Office: BA6214 (Bahen Center)

I am an assistant professor at the University of Toronto.

Previously I was a postdoctoral fellow at Harvard University from 2021-2024, and at SLMath in the Fall of 2024.

My research interests lies in complex geometry, geometric analysis, and nonlinear PDEs.

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