## IPMU Komaba Seminar

Date: | Tuesday, February 12, from 17:00 - 18:30 |

Place: | Room 056, Mathematical Sciences Building, Komaba Campus, The University of Tokyo |

Lecturer: | Katrin Wendland (University of Augsburg) |

Title: | "How to lift a construction by Hiroshi Inose to conformal field theory" |

Abstract: |
The moduli space of Einstein metrics is well known to algebraic and
differential geometers. Physicists have introduced the notion of
conformal field theories (CFTs) associated to K3, and the moduli space
of these objects is well understood as well. It can be interpreted as
a generalisation of the moduli space of Einstein metrics on K3, which
allows us to introduce this space without having to use background
knowledge from conformal field theory. However, just as no smooth
Einstein metrics on K3 are known explicitly, the explicit construction
of CFTs associated to K3 in general remains an open problem. The only
known constructions which allow to deal with families of CFTs give
CFTs associated to K3 surfaces with orbifold singularities. We use a classical construction by Hiroshi Inose to explicitly construct a family of CFTs which are associated to a family of smoot! h algebraic K3 surfaces. Although these CFTs were known before, it is remarkable that they allow a description in terms of a family of smooth surfaces whose complex structure is deformed while all other geometric data remain fixed. We also discuss possible extensions of this result to higher dimensional Calabi-Yau threefolds. |

Note: | This seminar is organized by Institute for the Physics and Mathematics of the Universe (IPMU) and Graduate School of Mathematical Sciences, The University of Tokyo. |