# Duong Hong Phong

Duong Hong Phong (Vietnamese: Dương Hồng Phong, born 30 August 1953) is an American mathematician of Vietnamese origin. He is a professor of mathematics at Columbia University. He is known for his research on complex analysis, partial differential equations, string theory and complex geometry.

## Education and career

After graduating from Lycée Jean-Jacques Rousseau in Saigon, Phong attended a university year at the École Polytechnique Fédérale, Lausanne, Switzerland and then went to the United States as an undergraduate and then a graduate student at Princeton University. From 1975 to 1977, he was an L. E. Dickson instructor at the University of Chicago.
In 1977, he defended his dissertation entitled "On Hölder and L$_p$ Estimates for the Conjugate Partial Equation on Strongly Pseudo-Convex Domains" under the direction of Elias Stein.
For the academic year 1977–1978, Phong was a researcher at the Institute for Advanced Study in Princeton, New Jersey. Since 1978, he has been at Columbia University. He served as the chair of the Columbia math department from 1995 to 1998.

## Recognition

In 1994, he was an Invited Speaker at the ICM in Zürich. He was the second Vietnamese to receive the honor (after Frédéric Pham).
In 2009 Phong was awarded the Stefan Bergman Prize for his research on the operators involved in the Neumann d-bar problem and on pseudo-differential operators.
In 2013, he was elected to the American Academy of Arts and Sciences.
He was named to the 2021 class of fellows of the American Mathematical Society "for contributions to analysis, geometry, and mathematical physics".
In 2024, he was elected to the National Academy of Sciences.

## Selected publications

* with C. Fefferman: On positivity of pseudo-differential operators. Proc Natl Acad Sci U S A. 1978 Oct; 75(10): 4673–4674. PMC 336181
* On integral representations for the Neumann operator. Proc Natl Acad Sci U S A. 1979 Apr; 76(4): 1554–1558. PMC 383427
* with C. Fefferman: On the lowest eigenvalue of a pseudo-differential operator. Proc Natl Acad Sci U S A. 1979 Dec; 76(12): 6055–6056. PMC 411799
* with C. Fefferman: On the asymptotic eigenvalue distribution of a pseudo-differential operator. Proc Natl Acad Sci U S A. 1980 Oct; 77(10): 5622–5625. PMC 350120
* with C. Fefferman: Symplectic geometry and positivity of pseudo-differential operators. Proc Natl Acad Sci U S A. 1982 Jan; 79(2): 710–713. PMC 345817
* with E. M. Stein: Singular integrals related to the Radon transform and boundary value problems. Proc Natl Acad Sci U S A. 1983 Dec; 80(24): 7697–7701. PMC 534412
* with E. M. Stein. "Hilbert integrals, singular integrals, and Radon transforms I." Acta Mathematica 157, no. 1 (1986): 99–157. doi:10.1007/BF02392592
* with Eric D'Hoker: "The geometry of string perturbation theory." Reviews of Modern Physics 60, no. 4 (1988): 917 doi:10.1103/RevModPhys.60.917
* with E. M. Stein: "The Newton polyhedron and oscillatory integral operators." Acta Mathematica 179, no. 1 (1997): 105–152. doi:10.1007/BF02392721
* with Jacob Sturm: "Lectures on stability and constant scalar curvature." Current developments in mathematics 2007 (2009): 101–176. arXiv:0801.4179
* with Jacob Sturm: Regularity of geodesic rays and Monge-Ampère equations. Proc. Amer. Math. Soc. 138 (2010), 3637–3650. doi:10.1090/S0002-9939-10-10371-2
* with Jian Song and Jacob Sturm: "Complex Monge Ampere Equations." arXiv:1209.2203 (2012).
* with Pengfei Guan: Partial Legendre transforms of non-linear equations. Proc. Amer. Math. Soc. 140 (2012), 3831-3842. doi:10.1090/S0002-9939-2012-11210-9