  We show that the base spaces of the semiuniversal unfoldings of some weighted
homogeneous singularities can be identified with moduli spaces of
$A_\infty$-structures on the trivial extension algebras of the endomorphism
algebras of the tilting objects. The same algebras also appear in the Fukaya
categories of their mirrors. Based on these identifications, we discuss
applications to homological mirror symmetry for Milnor fibers, and give a proof
of homological mirror symmetry for an $n$-dimensional affine hypersurface of
degree $n + 2$ and the double cover of the $n$-dimensional affine space
branched along a degree $2n + 2$ hypersurface. Along the way, we also give a
proof of a conjecture of Seidel from math/0206155 which may be of independent
interest.
