Mirror Symmetry and Fano Manifolds
  We consider mirror symmetry for Fano manifolds, and describe how one can recover the classification of 3-dimensional Fano manifolds from the study of their mirrors. We sketch a program to classify 4-dimensional Fano manifolds using these ideas. 
Tom Coates, Alessio Corti, Sergey Galkin, Vasily Golyshev, Alexander   Kasprzyk
math.AG math.CA math.CO