AdS/CFT correspondence and GIT stablity

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A general existence result of toric Sasaki-Einstein metrics was established. As its application, an eternal solution of Kaehler Ricci flow was constructed on the canonical line bundle of toric Fano Manifolds.On polarized manifolds with non-discrete automorphisms, it is shown that there are integral invariants which obstruct asymptotic Chow semi-stability. Using them it is possible to show the existence of a toric Fano Kaehler-Einstein manifold which is asymptotically unstable. It has been shown by S.K.Donaldson that a polarized manifolds with constant scalar curvature and with discrete automorphisms is asymptotically Chow-stable.A universal lower diameter bound for compact shrinking Ricci solitons was obtained.