Abstract: The homogeneous complex Monge-Ampere (HCMA) equation is a central topic in understanding the uniqueness of canonical metrics in Kahler classes. Under the setting of ALE Kahler manifolds, one of the main difficulties is the asymptotic behaviors of solutions to HCMA equations. In this talk, I will give an introduction to canonical metric problems under the setting of ALE Kahler manifolds and give some technical details on the asymptotic behavior of the solution. The talk is based on the speaker’s upcoming work.