University of California, Irvine
Department of Mathematics
Distinguished Lecture Series
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, KÃ¤hler 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
Stability and Constant Scalar Curvature Metrics in Kahler Geometry: analytic methods
Wednesday, February 20th
Lecture at 3pm. Reception at 4pm
We discuss some recent developments in the problem of KÃ¤hler 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-AmpÃ¨re equation.