The SYZ mirror symmetry conjecture is one possible refinement of the original mirror symmetry conjecture relating Hodge numbers of mirror Calabi–Yau manifolds. The other is Kontsevich's homological mirror symmetry conjecture (HMS conjecture). These two conjectures encode the predictions of mirror symmetry in different ways: homological mirror symmetry in an algebraic way, and the SYZ conjecture in a geometric way.