  We discuss various topics on degenerations and special Lagrangian torus
fibrations of Calabi-Yau manifolds in the context of mirror symmetry. A
particular emphasis is on Tyurin degenerations and the Doran-Harder-Thompson
conjecture, which builds a bridge between mirror symmetry for Calabi-Yau
manifolds and that for quasi-Fano manifolds. The proof of the conjecture is of
interest in its own right and leads us to a few other related topics such as
SYZ mirror symmetry, theta functions and geometric quantization. Inspired by
the conjecture, we also propose a new construction of Landau-Ginzburg models by
splitting Calabi-Yau fibrations.

Algebraic Geometry;Symplectic Geometry