报告摘要：Bershadsky, Cecotti, Ooguri and Vafa constructed a real valued invariant for Calabi?Yau manifolds, which is now called the BCOV invariant. The BCOV invariant is conjecturally related to the Gromov?Witten theory via mirror symmetry. In this talk, we prove the conjecture that birational Calabi?Yau manifolds have the same BCOV invariant. We also build an analogue between the BCOV invariant and the motivic integration. The result presented in this talk is a joint work with Lie Fu.