Mirror symmetry for Berglund-Hübsch Milnor fibers

We explain how to calculate the Fukaya category of the Milnor fiber of a Berglund-Hübsch invertible polynomial, proving many cases of a conjecture of Yankı Lekili and Kazushi Ueda on homological mirror symmetry. As usual, we begin by calculating the “very affine” Fukaya category; afterwards, we deform it, generalizing an earlier calculation of David Nadler. The main step of our calculation may be understood as determining a certain canonical extension of a perverse schober.