Abstract: Initiated by Mabuchi, Semmes, and Donaldson, homogeneous complex Monge-Ampere (HCMA) equations become a central topic in understanding the uniqueness and existence of canonical metrics in Kähler classes. Under the setting of ALE Kähler manifolds, one of the main difficulties is to understand 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 Kähler manifolds and discuss the recent progress on this problem. I will present a new result on the asymptotic behavior of HCMA solutions and outline the proof of the result. (The paper will be available on arXiv very shortly.)

Biography: Qi Yao is currently a James H. Simons Instructor at Stony Brook University. He finished her PhD at the University of Munster in 2023, advised by Hans-Joachim Hein. His research interests lie in complex geometry and geometric analysis, focusing on problems related to canonical metrics on Kähler manifolds.

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