Lu Qi-Keng Conjectue and Hua Domain

The first part I talk about the motivation for Lu Qi-Keng conjecture and the results about the presence or absence of zeroes of the Bergman kernel function of a bounded domain in ${\mathbf{C}}^{\mathbf{n}}$. The second part I summarize the main results on Hua domains, such as the explicit Bergman kernel function, comparison theorem for the invariant metrics, explicit complete Einstein-K"ahler metrics, the equivalence between the Einstein-K"ahler metric and the Bergman metric etc.