02/19/2008 - 12:00am

University of California, Irvine
Department of Mathematics
Distinguished Lecture Series

Duong Phong
Columbia University

Duong H. Phong got his Ph.D. in 1977, and is now a professor of mathematics at Columbia University. His main research interests are partial differential equations, mathematical physics, and complex geometry. He is particularly known for contributions to the positivity of pseudo-differential operators, the theory of singular Radon transforms, the theory of degenerate oscillatory integral operators, a Hamiltonian formulation of soliton equations, the solution of Calogero-Moser systems for arbitrary simple Lie algebras, and string perturbation theory. Recently, he has been particularly active in aspects of complex analysis and geometry related to two-dimensional supergeometry, Kähler geometry, stability in geometric invariant theory, and geometric heat flows.

Stability and Constant Scalar Curvature Metrics in Kahler Geometry: a survey
Tuesday, February 19th
Reception at 3:30pm. Lecture at 4pm
MSTB 254

Stability and Constant Scalar Curvature Metrics in Kahler Geometry: analytic methods
Wednesday, February 20th
Lecture at 3pm. Reception at 4pm
MSTB 254

We discuss some recent developments in the problem of Kähler metrics of constant scalar curvature and stability in geometric invariant theory. In particular, we discuss various notions of stability, both finite and infinite-dimensional, and various analytic methods for the problem. These include estimates for energy functionals, density of states and Tian-Yau-Zelditch and Lu asymptotic expansions, geometric heat flows, and both a priori estimates and pluripotential theory for the complex Monge-Ampère equation.