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Institute for the Physics and Mathematics of the UniverseWPI

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.