Kyeong-Dong Park, Kähler-Einstein Metrics on Smooth Fano Symmetric Varieties with Picard Number One

Symmetric varieties are normal equivarient open embeddings of symmetric homogeneous spaces and they are interesting examples of spherical varieties. I will prove that all smooth Fano symmetric varieties with Picard number one admit Kähler-Einstein metrics using a combinatorial criterion for K-stability of Fano spherical varieties obtained by Delcroix. To this end, I will present their algebraic moment polytopes and the barycenter of each moment polytope with respect to the Duistermaat-Heckman measure. This talk is based on joint work with Jae-Hyouk Lee and Sungmin Yoo.