## IPMU Seminar on Mathematical Physics

Date: | Monday, December 17 17:00 - 18:30 |

Place: | Room 002, Mathematical Sciences Building Komaba Campus, The University of Tokyo |

Lecturer: | Ken-Ichi Yoshikawa (The University of Tokyo) |

Title: | Analytic torsion for Calabi-Yau threefolds |

Abstract: |
In 1994, Bershadky-Cecotti-Ooguri-Vafa conjectured that analytic
torsion
gives rise to a function on the moduli space of Calabi-Yau
threefolds and
that it coincides with the quantity $F_{1}$ in string theory.
Since the holomorphic part of $F_{1}$ is conjecturally the
generating function
of the counting problem of elliptic curves in the mirror Calabi-Yau
threefold,
this implies the conjectural equivalence of analytic torsion and the
counting
problem of elliptic curves for Calabi-Yau threefolds through mirror
symmetry. After Bershadsky-Cecotti-Ooguri-Vafa, we introduced an invariant of Calabi-Yau threefolds, which we obtained using analytic torsion and a Bott-Chern secondary class. In this talk, we will talk about the construction and some explicit formulae of this analytic torsion invariant. Some part of this talk is based on the joint work with H. Fang and Z. Lu. |