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Moduli of A-infinity structures Ueda, Kazushi
Description
The triangulated category of graded matrix factorizations for an exceptional unimodal singularity is known to have a tilting object by Kajiura-Saito-Takahashi and Lenzing-de la Pena. If we deform the singularity, then we lose the grading, which can be recovered by adding one more variable to the defining polynomial. The triangulated category of graded matrix factorizations of the resulting four-variable polynomial no longer has a tilting object, but has a classical generator, whose endomorphism algebra is the degree 2 trivial extension of the endomorphism algebra of the tilting object of the original category. In the talk, we will discuss the moduli space of A-infinity structures on this graded algebra, and its relation to 1. the positive part of the universal unfolding of the exceptional unimodal singularity, 2. the moduli space of K3 surfaces, and 3. homological mirror symmetry. If the time permits, we also discuss higher-dimensional generalizations and iterated singularity categories (i.e., singularity categories of singularity categories of ...) of non-isolated singularities. This is a joint work with Yanki Lekili.
Item Metadata
| Title |
Moduli of A-infinity structures
|
| Creator | |
| Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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| Date Issued |
2019-09-05T10:03
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| Description |
The triangulated category of graded matrix factorizations
for an exceptional unimodal singularity is known to have a tilting object
by Kajiura-Saito-Takahashi and Lenzing-de la Pena.
If we deform the singularity, then we lose the grading,
which can be recovered by adding one more variable
to the defining polynomial.
The triangulated category of graded matrix factorizations
of the resulting four-variable polynomial no longer has a tilting object,
but has a classical generator,
whose endomorphism algebra is the degree 2 trivial extension
of the endomorphism algebra of the tilting object
of the original category.
In the talk, we will discuss the moduli space of A-infinity structures
on this graded algebra, and its relation to
1. the positive part of the universal unfolding of the exceptional
unimodal singularity,
2. the moduli space of K3 surfaces, and
3. homological mirror symmetry.
If the time permits, we also discuss higher-dimensional generalizations
and iterated singularity categories
(i.e., singularity categories of singularity categories of ...)
of non-isolated singularities.
This is a joint work with Yanki Lekili.
|
| Extent |
52.0 minutes
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| Subject | |
| Type | |
| File Format |
video/mp4
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| Language |
eng
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| Notes |
Author affiliation: University of Tokyo
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| Series | |
| Date Available |
2020-03-04
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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| DOI |
10.14288/1.0388857
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| URI | |
| Affiliation | |
| Peer Review Status |
Unreviewed
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| Scholarly Level |
Researcher
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| Rights URI | |
| Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International