Log degenerations of LG models for toric orbifolds and 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 that 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.