Plane curve singularities and combinatorics of quivers

I will discuss a recently discovered (and largely mysterious) connection between the topology of isolated singularities of plane curves and their morsifications (V. Arnold, N. A'Campo, S. Gusein-Zade) and the mutation equivalence of quivers associated with their morsifications.
The talk will be accessible to a general mathematical audience. Joint work with P. Pylyavskyy, E. Shustin, and Dylan Thurston, arXiv:1711.10598.