Milnor fibers of real singularities

Milnor fibers of isolated hypersurface singularities carry the most important information on the singularity. We review the works by A'Campo and Gusein-Zade, who showed that, in the case of real plane curve singularities, one can use special deformations (so-called morsifications) in order to recover the topology of the Milnor fiber, intersection form in vanishing homology, monodromy operator and other invariants. We prove that any real plane curve singularity admits a morsification and discuss its relation to the Milnor fiber, which is still an open problem of the complex-analytic nature. Joint work with P. Leviant.