Abstract for the talk at 30.01.2004 (13:30 h)

Xiaonan Ma (Ecole Polytechnique, Palaiseau, France)

Bergman kernel, Heat kernel and constant scalar curvature

Let L be a positive holomorphic line bundle on a compact Kähler manifold X. The Bergman kernel is with an orthonormal basis of . Theorem (Zelditch) : There exist soomfunction on X such that as , has the asymptotic expansion . It plays a very important role in Donaldson's work on the relation of constant scalar curvature and the balance condition for the projective embedding.

In this talk, I will explain how to get Zelditch's Theorem from the asymptotic expansion of the heat kernel, and its generalization to the symplectic case.