## IPMU Seminar on Mathematical Physics

Date: | Monday, October 29 17:00 - 18:30 |

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

Speaker: | Hiroshige Kajiura (RIMS, Kyoto University) |

Title: | Some examples of triangulated and/or $A_\infty$-categories related to homological mirror symmetry |

Abstract: | In this talk, I would like to discuss on some examples of
triangulated and/or $A_\infty$-categories associated to
manifolds with additional structures
(symplectic structure, complex structure, ...)
which can appear in the homological mirror symmetry (HMS) set-up
proposed by Kontsevich'94. The strongest form of the HMS may be to show the equivalence of Fukaya category on a symplectic manifold with the category of coherent sheaves on the mirror dual complex manifold at the level of $A_\infty$-categories. On the other hand, for a given $A_\infty$-category, there is a canonical way (due to Bondal-Kapranov, Kontsevich) to construct an enlarged $A_\infty$-category whose restriction to the zero-th cohomology forms a triangulated category. I plan to talk about the triangulated structure of categories associated to regular systems of weights (joint work with Kyoji Saito and Atsushi Takahashi), and also give a realization of higher $A_\infty$-products in Fukaya categories from the mirror dual complex manifold via HMS in some easy examples. |