Conference on Complex Analysis, Differential Geometry, and Partial Differential Equations
This is a week-long conference on the many aspects of complex analysis, differential geometry, and partial differential equations centered around the theme of canonical metrics in geometry. Of particular importance are recent developments such as multiplier ideal sheaves, Bergman kernels and asymptotic stability in geometric invariant theory, Hamiltonian dynamics and complex Monge-Ampere equations, geometric heat flows, and energy functionals.
Canonical metrics involve typically a non-linear system of partial differential equations, where the unknown is a tensor. They arise from geometry and topology, but they are also closely to basic equations from theoretical physics such as Yang-Mills equations and Einstein's equations in general relativity. They are usually very difficult to solve, but there has been recently an influx of new ideas from many different directions. This conference will help cross-fertilization of ideas between the leading experts, and introduce a new generation of young students and postdoctoral researchers to problems and methods in the area.
