  The variation operator in singularity theory maps relative homology cycles to
compact cycles in the Milnor fiber using the monodromy. We construct its
symplectic analogue for an isolated singularity. We define a new Floer
cohomology, called monodromy Lagrangian Floer cohomology, which provides
categorifications of the standard theorems on the variation operator and the
Seifert form. The key ingredients are a special class $\Gamma$ in the
symplectic cohomology of the inverse of the monodromy and its closed-open
images. For isolated plane curve singularities whose A'Campo divide has depth
zero, we find an exceptional collection consisting of non-compact Lagrangians
in the Milnor fiber corresponding to a distinguished collection of vanishing
cycles under the variation operator.
