## Kavli IPMU Komaba Seminar

Date, time & place Monday 16:30 - 18:00 002Room #002 (Graduate School of Math. Sci. Bldg.)

### 2007/12/17

17:00-18:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Ken-Ichi Yoshikawa (The University of Tokyo)
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.