The Seven Elementary Catastrophes and Physical Applications

In this seminar, I will give an introduction to catastrophe theory and derive Thom’s “seven elementary catastrophes” in the physicist’s (rather than mathematician’s) language. Starting from critical points and structural stability, I will derive the characteristic geometries of the caustics and discuss how they arise in various physical contexts (e.g. optics, cosmological structure formation or quantum mechanics). I will also show some artwork by Salvador Dalí and touch upon Picard-Lefschetz theory and the ADE classification. Time allowing, I would finally like to present some of my research on the cosmic web in the caustic skeleton model.