Degenerations of K\"ahler-Einstein Fano Manifolds
  In this Thesis, I investigate how Fano manifolds equipped with a Kahler-Einstein metric can degenerate as metric spaces (in the Gromov-Hausdorff topology) and some of the relations of this question with Algebraic Geometry, in particular in the direction of the study of moduli spaces and their compactifications. 
Cristiano Spotti
math.DG math.AG