The flexibility of caustics and its applications

I will begin by reviewing the story of the flexibility of singularities of smooth mappings, from the immersion theory of Smale-Hirsch to the Igusa-Lurie contractibility of the space of framed functions. I will then explain similar flexibility results for caustics: the singularities of wavefronts, and discuss its applications to symplectic and contact topology, notably to the arborealization program for skeleta of Weinstein manifolds.

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https://people.math.harvard.edu/~gammage/ons/