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Kavli IPMU Komaba Seminar
過去の記録 ～04/24｜次回の予定｜今後の予定 04/25～
| 開催情報 | 月曜日 16:30～18:00 数理科学研究科棟(駒場) 002号室 |
|---|---|
| 担当者 | 河野 俊丈 |
2007年10月29日(月)
17:00-18:30 数理科学研究科棟(駒場) 002号室
Hiroshige Kajiura 氏 (RIMS, Kyoto University)
Some examples of triangulated and/or $A_\\infty$-categories
related to homological mirror symmetry
Hiroshige Kajiura 氏 (RIMS, Kyoto University)
Some examples of triangulated and/or $A_\\infty$-categories
related to homological mirror symmetry
[ 講演概要 ]
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.
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.
