Abstract

After the discovery of the Bergman kernel by Stefan Bergman, many researchers tried to find complex domains whose Bergman kernels can be expressed explicitly. However, except some special cases, it is difficult to compute this kernel function. In this talk, I will introduce some basic methods to compute Bergman kernels with simple examples.

If time permits, I will give another proof of Poincare's theorem on the holomorphic inequivariance of the unit ball and the polydisk by using explicit forms of the Bergman kernels of these domains.