EVENT DETAILS AND ABSTRACT

Title: Szego kernels and Poincare series
Speaker: Zhiqin Lu
Speaker Info: UC Irvine
Brief Description:
Special Note:
Abstract:

I shall talk about the relations between the Bergman kernels on a compact Kahler manifold and the Bergman kernels on its universal cover. We prove that the summation of the Bergman kernels (over the fundamental group) on the universal cover is equal to the Bergman kernels on the compact manifold, a result that was known only for the case of locally Hermitian symmetric spaces. Using the result, we give a simple proof of Napier's holomorphic convexity theorem and prove the surjectivity of the Poincare map. This is joint work with S. Zelditch.