Catastrophe Theory

What it is about

You will learn the theory of critical points and their local classifications, in particular nondegenerate and certain degenerate singularities such as fold and cusp. In the end you will be familiar with classification theorems for germs and with stable unfoldings (unfoldings) up to codimension 4.

What you will be able to do

• Familiarity with nondegenerate critical points and the Morse lemma
• Understanding of fold- and cusp-singularities
• Knowledge of reduction lemma, determinacy and codimension
• Application of classification theorems for germs up to codimension 4
• Understanding of stable unfoldings (unfoldings)

What the module consists of

• VorlesungDelivery of content through lectures and demonstrative examples; discussion to motivate own analyses
• Übung/PraktikumExercises on lecture content with problem sheets and solutions for deepening and self-check

Teaching method

• Vortrag mit Beispielen und Diskussionto present content, illustrate it and motivate students to own analysis
• Begleitende Übungssitzungen mit Übungsblättern und Lösungento deepen methods and to independently assess learning progress