The flexibility of caustics and its applications

Singularities of smooth maps are flexible: there holds an h-principle for their simplification. I will discuss an analogous h-principle for caustics, i.e. the singularities of Lagrangian and Legendrian wavefronts. I will also discuss applications, notably to Nadler's arborealization program for skeleta of Weinstein manifolds, which can be thought of as a high-dimensional symplectic generalization of the theory of ribbon graphs in open Riemann surfaces.