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Kavli IPMU Komaba Seminar
Seminar information archive ～06/27｜Next seminar｜Future seminars 06/28～
| Date, time & place | Monday 16:30 - 18:00 002Room #002 (Graduate School of Math. Sci. Bldg.) |
|---|
2007/10/29
17:00-18:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Hiroshige Kajiura (RIMS, Kyoto University)
Some examples of triangulated and/or A_\\infty-categories
related to homological mirror symmetry
Hiroshige Kajiura (RIMS, Kyoto University)
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.
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.
