Compact Moduli Spaces of Del Pezzo Surfaces and K\"ahler-Einstein   metrics
  We prove that the Gromov-Hausdorff compactification of the moduli space of Kahler-Einstein Del Pezzo surfaces in each degree agrees with certain algebro-geometric compactification. In particular, this recovers Tian's theorem on the existence of Kahler-Einstein metrics on smooth Del Pezzo surfaces and classifies the degenerations of such metrics. The proof is based on a combination of both algebraic and differential geometric techniques. 
Yuji Odaka, Cristiano Spotti, and Song Sun
math.DG math.AG