• Title, Summary, Keyword: matrix factorizations

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EQUIVARIANT MATRIX FACTORIZATIONS AND HAMILTONIAN REDUCTION

  • Arkhipov, Sergey;Kanstrup, Tina
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.5
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    • pp.1803-1825
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    • 2017
  • Let X be a smooth scheme with an action of an algebraic group G. We establish an equivalence of two categories related to the corresponding moment map ${\mu}:T^{\ast}X{\rightarrow}g^{\ast}$ - the derived category of G-equivariant coherent sheaves on the derived fiber ${\mu}^{-1}(0)$ and the derived category of G-equivariant matrix factorizations on $T^{\ast}X{\times}g$ with potential given by ${\mu}$.

Relaxed multisplitting and relaxed nonstationary two-stage multisplitting methods

  • 윤재헌
    • Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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    • pp.5.1-5
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    • 2003
  • In this paper, we study the convergence of relaxed multisplitting and relaxed nonstationary two-stage multisplitting methods associated with a multisplitting which is obtained from the ILU factorizations for solving a linear system whose coefficient matrix is an H-matrix. Also, parallel performance results of relaxed nonstaionary two-stage multisplitting method using ILU factorizations as inner splittings on the IBM p690 supercomputer are provided to analyze theoretical results.

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THE GENERALIZED PASCAL MATRIX VIA THE GENERALIZED FIBONACCI MATRIX AND THE GENERALIZED PELL MATRIX

  • Lee, Gwang-Yeon;Cho, Seong-Hoon
    • Journal of the Korean Mathematical Society
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    • v.45 no.2
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    • pp.479-491
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    • 2008
  • In [4], the authors studied the Pascal matrix and the Stirling matrices of the first kind and the second kind via the Fibonacci matrix. In this paper, we consider generalizations of Pascal matrix, Fibonacci matrix and Pell matrix. And, by using Riordan method, we have factorizations of them. We, also, consider some combinatorial identities.

COMPARISON OF MIRROR FUNCTORS OF ELLIPTIC CURVES VIA LG/CY CORRESPONDENCE

  • Lee, Sangwook
    • Journal of the Korean Mathematical Society
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    • v.57 no.5
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    • pp.1135-1165
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    • 2020
  • Polishchuk-Zaslow explained the homological mirror symmetry between Fukaya category of symplectic torus and the derived category of coherent sheaves of elliptic curves via Lagrangian torus fibration. Recently, Cho-Hong-Lau found another proof of homological mirror symmetry using localized mirror functor, whose target category is given by graded matrix factorizations. We find an explicit relation between these two approaches.