Log Hodge Theoretic Formulation of Mirror Symmetry for Calabi-Yau Threefolds

We hope to understand the Hodge theoretic aspect of mirror symmetry in the framework of the fundamental diagram of log mixed Hodge theory. We give a formulation of mirror conjecture for Calabi-Yau threefolds as the coincidence of log period maps with specified sections under the mirror map. Since a variation of Hodge structure with unipotent monodromies on a product of punctured discs uniquely extends over the puncture to a log Hodge structure, we can work on the boundary point over which the log Riemann-Hilbert correspondence exists, and we can observe clearly in high resolution the behavior of Zstructure over the boundary point (cf. notes in Introduction below). This is an advantage of log Hodge theory.