Andrew Hwang - Construction of Circle-Invariant Kahler Metrics

In the total space of an Hermitian disk bundle, it is possible to construct a Kahler metric from a single function of one variable by using an ansatz of Calabi. A change of coordinates closely related to a Legendre transform converts the scalar curvature operator for such a metric into a very simple linear second-order operator; it is thereby possible to construct metrics of specified scalar curvature. I will describe these methods and their limitations. (Mostly joint work with Michael A. Singer, University of Edinburgh.)