|DATE||February 15 (Tue), 2022|
|TITLE||Explicit computation of the Bergman kernel for some non-homogeneous domains|
|ABSTRACT||The Bergman kernel function is an important tool in several complex variables. It is defined for any bounded domains in C^n, but it is difficult to find the explicit form of the Bergman kernel function K_D(z, w) for any given domain D. It is known that each bounded homogeneous domain has an explicit form of the Bergman kernel function.
In this talk, we explain the methods of computing the Bergman kernel functions for some non-homogeneous domains. We focus on the Hartogs domains, Hartogs triangles, complex ellipsoids and intersection of cylindrical domains. The methods of computing the kernels for each domain will be explained using the hypergeometric series. Also we discuss the existence of zeros of the Bergman kernel functions.