Speculations about homological mirror symmetry for affine hypersurfaces

The wrapped Fukaya category of an algebraic hypersurface $H$ in $(C*)^n$ is conjecturally related via homological mirror symmetry to the derived category of singularities of a toric Calabi-Yau manifold $X$, whose moment polytope is determined by the tropicalization of $H$. (The case of the pair of pants discussed in the first talk is a special case of this construction). In this talk we will outline some further speculative ideas concerning "relative" homological mirror symmetry for pairs $((C*)^n, H)$ and wrapped Fukaya categories of higher-dimensional pairs of pants.