Homological Berglund-Hübsch mirror symmetry for curve singularities

Given a two-variable invertible polynomial, we show that its category of maximally-graded matrix factorisations is quasi-equivalent to the Fukaya–Seidel category of its Berglund–Hübsch transpose. This was previously shown for Brieskorn–Pham and D-type singularities by Futaki–Ueda. The proof involves explicit construction of a tilting object on the B‑side, and comparison with a specific basis of Lefschetz thimbles on the A‑side