Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fukaya category for Landau-Ginzburg orbifolds and Berglund-H\"ubsch
  conjecture for invertible curve singularities   For a weighted homogeneous polynomial and a choice of a diagonal symmetry
group, we define a new Fukaya category based on the wrapped Fukaya category of
its Milnor fiber together with monodromy information. It is analogous to the
variation operator in singularity theory. As an application, we formulate a
full version of Berglund-H\"ubsch homological mirror symmetry and prove it for
the case of two variables. Namely, given one of the polynomials $W= x^p+y^q,
x^p+xy^q,x^py+xy^q$ and a symmetry group $G$, we use Floer theoretic
construction to obtain the transpose polynomial $W^T$ with the transpose
symmetry group $G^T$ as well as derived equivalence between the new Fukaya
category of $(W,G)$ and the matrix factorization category of $(W^T, G^T)$. In
this case, monodromy corresponds to the restriction of LG model to a
hypersurface in the mirror. For ADE singularities, Auslander-Reiten quivers for
indecomposable matrix factorizations were known from 80's, and we find the
corresponding Lagrangians as well as surgery exact triangles.

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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: stat