Noncommutative homological mirror functor

Cheol Hyun Cho, Hansol Hong, Siu Cheong Lau

Research output: Contribution to journalArticlepeer-review


We formulate a constructive theory of noncommutative Landau-Ginzburg models mirror to symplectic manifolds based on Lagrangian Floer theory. The construction comes with a natural functor from the Fukaya category to the category of matrix factorizations of the constructed Landau-Ginzburg model. As applications, it is applied to elliptic orbifolds, punctured Riemann surfaces and certain non-compact Calabi-Yau threefolds to construct their mirrors and functors. In particular it recovers and strengthens several interesting results of Etingof-Ginzburg, Bocklandt and Smith, and gives a unified understanding of their results in terms of mirror symmetry and symplectic geometry. As an interesting application, we construct an explicit global deformation quantization of an affine del Pezzo surface as a noncommutative mirror to an elliptic orbifold.

Original languageEnglish
Pages (from-to)1-111
Number of pages111
JournalMemoirs of the American Mathematical Society
Issue number1326
Publication statusPublished - 2021

Bibliographical note

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics


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