Duong H. Phong

Professor of Mathematics. Phong has made fundamental contributions to string theory, geometry, and analysis. In string theory, Phong and E. D'Hoker did a pioneering and celebrated calculation of two-loop scattering amplitudes. This required fundamental new ideas. Another very important contribution by Phong and D'Hoker is a much deeper understanding of the one-loop amplitude than had been possible earlier. They elucidated its subtle analytic behavior and relation to unitarity in quantum field theory. Both contributions, though 10 and 20 years old, respectively, remain the gold standard in their respective areas. Phong and D'Hoker are also known for their solution of supersymmetric gauge theories with matter in the adjoint representation for all simple Lie groups, requiring the construction of Lax pairs with spectral parameter for elliptic Calogero-Moser systems with arbitrary Lie algebras, a problem that had stood open for some 20 years. They also found new links between Seiberg-Witten theory and the theory of integrable models. In geometry and analysis, Phong is known for the development of the theory of singular Radon transforms (with E.M. Stein); the development of a systematic approach to estimates for partial differential equations, based on microlocalization and canonical transformations (with C. Fefferman); and important progress on some fully non-linear equations and the problem of canonical metrics in K�hler geometry (with J. Sturm et al).