## IPMU Mathematics seminar in Kashiwa

Date: | May 29, 2008, 15:30 - 17:00 |

Place: | Room 630, 6th floor, Research Centers Building, Kashiwa Campus of the University of Tokyo |

Speaker: | Masahito Yamazaki (Univ. of Tokyo) |

Title: | Quivers, brane tilings and toric Calabi-Yau/Sasaki-Einstein geometry |

Abstract: |
In string theory, there is a remarkable conjecture that the
study of quivers is in a sense "equivalent" to
toric Sasaki-Einstein geometry or its cone toric Calabi-Yau geometry. In this talk, I will report on possible mathematical formulation of this conjecture. First, I will present categorical formulation of this equivalence (joint work with Kazushi Ueda). In this discussion, bipartite graphs on two-dimensional torus, known as brane tilings, play crucial roles. I will also describe the relation of quivers and brane tilings to Sasaki-Einstein geometry, and explain the equivalence of the "a-function" of quiver with relations and the volume of Sasaki-Einstein manifold. |