K-Stability and Sasaki-Einstein Metrics

Explore the intricate relationship between K-stability and Sasaki-Einstein metrics in this 58-minute conference talk delivered at ICBS2025. Delve into advanced concepts in differential geometry and algebraic geometry as the speaker examines the stability conditions for Kähler manifolds and their connections to Sasaki-Einstein structures. Learn about the theoretical foundations of K-stability, understand how it applies to the existence of canonical metrics, and discover the geometric properties of Sasaki-Einstein manifolds. Gain insights into current research developments in this specialized area of mathematics, including the interplay between algebraic and differential geometric approaches to understanding these complex geometric structures.