Deep Morin Singularities of the McKean-Scovel Operator

The McKean-Scovel operator is the simplest nonlinear Sturm-Liouville operator acting on functions satisfying Dirichlet boundary conditions: its nonlinearity is just taking the square of the incoming function. This text contains a proof of a conjecture from the late ´80: its critical set consists only of Morin singularities, which attain arbitrary depth.