DMM seminar

Speaker: Kenichi Yoshikawa (Kyoto U)
Title: Analytic torsion for Borcea-Voisin threefolds
Date (JST): Mon, Nov 17, 2014, 14:00 - 17:00
Place: Seminar Room A
Abstract: In 1994, Bershadsky-Cecotti-Ooguri-Vafa discovered a remarkable (conjectural) equivalence between certain curve counting invariants and analytic torsion for Calabi-Yau threefolds. After BCOV, Fang, Lu and I introduced a holomorphic torsion invariant for Calabi-Yau threefolds, which we call
``BCOV invariant''. In my talk, I would like to explain the recent progress in the study of BCOV invariants.

In the first part, after recalling the definition of analytic torsion and some interesting examples, I will explain the construction of BCOV invariants and formulate the BCOV conjecture.

In the second part, I explain an explicit formula for the BCOV invariants for Calabi-Yau threefolds of Borcea-Voisin. The BCOV invariants of Borcea-Voisin threefolds are reduced to the holomorphic torsion invariants of K3 surfaces with involution, which was introduced in 2004. I give an explicit formula for this last invariants, which is expressed by an explicit Borcherds product and an explicit Siegel modular form. This result of the holomorphic torsion invariants for K3 surfaces with involution is a joint work with Shouhei Ma.
Remarks: 15:00-15:30 break