Catastrophe Theory

Explore catastrophe theory in this comprehensive lecture by Connor McCranie and Markus Pflaum. Begin with an introduction to René Thom's catastrophe theory, covering definitions of degenerate and non-degenerate critical points in smooth functions. Delve into the algebra of germs of smooth real-valued functions and learn how to describe singular germs within this framework. Examine the classification theorem of critical points up to codimension 4 using germ language. Study unfoldings and the universal unfoldings for the seven elementary catastrophes, including explanations of the catastrophe set and bifurcation set. Visualize abstract concepts through practical examples and conclude with an application of catastrophe theory in chemistry. This in-depth presentation covers topics such as the Morse Lemma, classification of critical points, structure of unfoldings, and provides relevant references for further study.