Positive Sasakian structures on 5-manifolds
  The aim of this paper is to study compact 5--manifolds which carry a positive Sasakian structure. Strong restrictions are derived for the integral homology groups. In some cases, all positive Sasakian structures are classified. A key step is to study log Del Pezzo surfaces whose boundary divisor contains positive genus curves. 
J\'anos Koll\'ar (Princeton Univ)