Homological mirror symmetry for Milnor fibers of simple singularities

Abstract

We prove homological mirror symmetry for Milnor fibers of simple singularities, which are among the log Fano cases of Conjecture 1.5 in arXiv:1806.04345. The proof is based on a relation between matrix factorizations and Calabi--Yau completions. As an application, we give an explicit computation of the symplectic cohomology group of the Milnor fiber of a simple singularity in all dimensions.