Joonyeong Won, K-stability, Kähler-Einstein Metric on Fano Varieties and Sasaki-Einstein Metric on 5-dimensional Smale Manifolds

We discuss on recent progresses of the existence problem of Kähler-Einstein metric on Fano varieties by K-stability of them and also the existence problem of Sasaki-Einstein metric on 5-dimensional Smale manifolds via K-stability of weighted hypersurface log del Pezzo surfaces.