EVENT DETAILS AND ABSTRACT

Title: Positivity of direct image bundles and geodesics in the space of Kahler potentials
Speaker: Bo Berndtsson
Speaker Info: Chalmers Inst. of Technology
Brief Description:
Special Note:
Abstract:

We first review a general result on positivity of vector bundles that arise as direct images of (semi)ample line bundles. Applied to the special case of products, X=ΩxZ, where Ω is an annulus, and direct images under the projection map to Ω, this gives a way to estimate the L²-norms defined by geodesics in the space of Kahler potentials on Z. We use this method to prove a theorem on approximation of geodesics by Bergman kernels - refining earlier work of Phong and Sturm) - and also to prove a theorem on approximation of certain probability measures that we associate to geodesics - generalizing recent work of Chen and Sun.