Dubrovin's conjecture for FJRW theory

Let $(W,G)$ be an admissible Landau–Ginzburg pair, with $W$ a nondegenerate quasihomogeneous polynomial and $G$ an admissible subgroup of its maximal symmetry group containing the exponential grading element. Let ${\mathcal H}_{W,G}$ be the FJRW state space, and let $n$ be its rank. Dubrovin conjecture in FJRW theory. The derived category of $G$-equivariant matrix factorizations of $W$ admits a full system of $n$ exceptional objects if and only if the FJRW theory of $(W,G)$ is semisimple. This is proposed as an FJRW analogue of Dubrovin's conjecture relating exceptional collections and semisimple quantum cohomology; the paper notes that the assertion is known for certain groups and invertible polynomials but is not established in general.