We prove an equivalence of two -functors, via Orlov’s Landau–Ginzburg/ Calabi–Yau (LG/CY) correspondence. One is the Polishchuk–Zaslow mirror symmetry functor of elliptic curves, and the other is a localized mirror functor from the Fukaya category of to a category of noncommutative matrix factorizations. As a corollary, we prove that the noncommutative mirror functor realizes homological mirror symmetry for any t.
"Noncommutative homological mirror symmetry of elliptic curves." Kyoto J. Math. 61 (3) 723 - 743, September 2021. https://doi.org/10.1215/21562261-2020-0001