Homological mirror symmetry for Berglund–Hübsch mirror pairs

Let $W$ be an invertible weighted homogeneous polynomial in $n+1$ variables, let $\check{W}$ be its Berglund–Hübsch transpose polynomial, and let $\Gamma_W$ be the group acting diagonally on the variables. Write $\mathcal W(\check{W}^{-1}(1))$ for the wrapped Fukaya category of the Milnor fiber $\check{W}^{-1}(1)$, and let $\operatorname{mf}(\mathbb{C}^{n+2},\Gamma_W,W+x_0x_1\cdots x_{n+1})$ denote the dg-category of $\Gamma_W$-equivariant matrix factorizations. Homological mirror symmetry conjecture. There is a quasi-equivalence of idempotent complete $A_{\infty}$-categories

$$\mathcal W(\check{W}^{-1}(1))\simeq \operatorname{mf}(\mathbb{C}^{n+2},\Gamma_W,W+x_0x_1\cdots x_{n+1}).$$

This is a homological mirror symmetry prediction for Berglund–Hübsch mirror pairs, relating the wrapped Fukaya category of the Milnor fiber to an equivariant matrix-factorization category. The supplied evidence states that, under a vanishing condition on Hochschild cohomology, the conjectural equivalence leads to corresponding symplectic and Hochschild cohomology results; the claim itself is recorded as resolved in the source metadata.