## Welcome to Freid Tong's Homepage

# Contact Information

Department of Mathematics

University of Toronto

40 St. George St.

Toronto, Ontario, Canada

Email: freid.tong@utoronto.ca

(My Harvard email has been deactivated.)

# About me

This semester, I am at SLMath/MSRI as a postdoctoral fellow. Starting January 2025, I will be an assistant professor at the University of Toronto.

Previously I was a postdoctoral fellow at Harvard University from 2021-2024.

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

In Spring 2025, I will be teaching MAT458/MAT1001: Real Analysis II.

# Education

Ph.D. in Mathematics, Columbia University, 2016-2021. Advisor: Prof. D.H. Phong

B.S. in Mathematics with high distinction, University of Toronto, 2012-2016.

# Publication and Preprints

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

# Past Teaching/Mentoring

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

# Seminars and Workshops

CMSA Member's Seminar Fall 2022, Harvard's CMSA

CMSA Member's Seminar 2021-2022, Harvard's CMSA

Informal Complex Geometry and PDE Seminar, Columbia University

Student Geometric Analysis Seminar, Columbia University