Kewei Zhang，Peking University

The existence of Kahler-Einstein metrics is equivalent to the solvability of certain complex Monge-Ampere equations, which however is often obstructed by certain stability conditions of the under lying manifold. In this series of talks we will present a quantization approach that directly relates certain stability thresholds to the existence Kahler-Einstein metrics. This approaches simplifies some arguments in the Yau-Tian-Donaldson literature and also yields some new criteria for the existence of canonical metrics.