Xiaonan Ma, Ecole Polytechnique, France

Heat kernel, Bergman kernel and constant scalar curvature

By using the asymptotic expansion of the Bergman kernel, Donaldson found that the existence of Kähler metrics with constant scalar curvature is shown to be closely related to Chow-Mumford stability.

In this talk, we establish the asymptotic expansion of the Bergman kernel  in the general context of symplectic manifolds and orbifolds. We use some techniques from the local index theory (or the heat kernel). One motivation of our work is to extend Donaldson's work to orbifolds and to understand the relationship between heat kernel, index formula and stability.