Welcome to Freid Tong's Homepage

About me

I am an assistant professor at the University of Toronto. 

My research is in complex geometry, geometric analysis, and nonlinear PDEs. Here is my CV. 

This semester, I am teaching MAT337: Introduction to Real Analysis. 

Seminars and Events

• Fields Geometric Analysis Colloquium

• UofT Geometry and Topology Seminar

• Workshop on Calabi-Yau metrics and optimal transportation, Summer 2026

Publication and Preprints

• (with T.C. Collins) Boundary regularity of optimal transport maps on convex domains. arXiv

• (with Y. Chen, S.K. Chiu, M. Hallgren, G. Szekelyhidi, and T.D. To) On Kahler-Einstein currents. arXiv 

• (with T.C. Collins and S.T. Yau) A free-boundary Monge-Ampere equation and applications to complete Calabi-Yau metrics. arXiv

• (with S.T. Yau) Generalized Monge-Ampere functionals and related variational problems. arXiv

• (with B. Guo, D.H. Phong and C. Wang) On the modulus of continuity of solutions to complex Monge-Ampere equations. arXiv 

• (with B. Guo, D.H. Phong and C. Wang) On L^∞ estimates for Monge-Ampere and Hessian equations on nef classes. Analysis & PDE. (2024) arXiv 

• (with B. Guo and K. Smith) On the Hessian-cscK equations. Math. Z. (2023) arXiv

• (with B. Guo and D.H. Phong) Stability estimates for the complex Monge-Ampere and Hessian equations. Calculus of Variations and PDEs. (2023). arXiv

• (with B. Guo and D.H. Phong) A new gradient estimate for the complex Monge-Ampere equation. Math. Ann. (2022). arXiv

• (with B. Guo and D.H. Phong) On L^∞ estimates for complex Monge-Ampere equations. Annals of Math. (2023). arXiv

• (with T.C. Collins and B. Guo) On the degeneration of asymptotically conical Calabi-Yau metrics. Math. Ann. (2022). arXiv

• A new positivity condition for the curvature of Hermitian manifolds. Math. Z. (2021). arXiv

• (with S. Huang, M.-C. Lee and L.F. Tam) Longtime existence of Kähler-Ricci flow and holomorphic sectional curvature. Comm. Anal. Geom. (2023) arXiv

• The Kähler-Ricci flow on manifolds with negative holomorphic curvature. arXiv

Past Teaching

• Winter 2025: MAT458/MAT1001: Real Analysis II

• Fall 2023: Topics in Geometric PDEs (Harvard University)

• Fall 2022: Integration, Series and Differential Equations (Harvard University)

• Summer 2021: Linear Algebra (Columbia University)

• Summer 2019, 2020: Calculus IV (Columbia University)