Analytic torsion and geometry of moduli spaces

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We studied the BCOV invariant of Calabi-Yau threefolds and we determined its explicit formula in some important cases. One of our major progresses is the determination of the BCOV invariant of quantic mirror threefolds, which verified some part of the conjecture of Bershadsky-Cecotti-Ooguri-Vafa. Another major progress is the computation of the BCOV invariant of Borcea-Voisin threefolds of exceptional type, which verified the conjecture of Harvey-Moore in these cases. To obtain these results, we studied the behavior of Quillen metrics for degenerating families of varieties. In particular, we determined the singularity of Quillen metrics for one-parameter degenerating families.