Morsifications of real singularities and beyond

Morsifications of real plane curve singularities, i.e., deformations with the maximal possible numer of real hyperbolic nodes, have been introduced in 70th by N. A'Campo and S, Gusein-Zade for computing important singularity invariants. We discuss the (still open) existence problem for morsifications, possible extensions to higher dimensions, and recently discovered relations to combinatorics of quivers that appears in the theory of cluster algebras. Based on joint works with P. Leviant and with S. Fomin, P. Pylyavskyy and D. Thurston.