Logarithmic degenerations of Landau-Ginzburg models for toric orbifolds   and global tt^* geometry
  We discuss the behavior of Landau-Ginzburg models for toric orbifolds near the large volume limit. This enables us to express mirror symmetry as an isomorphism of Frobenius manifolds which aquire logarithmic poles along a boundary divisor. If the toric orbifold admits a crepant resolution we construct a global moduli space on the B-side and show that the associated tt^*-geometry exists globally. 
Etienne Mann, Thomas Reichelt
math.AG