Henry Adams and Enrique Alvarado - An Introduction to Morse Theory

Explore the fundamentals of Morse theory in this 40-minute lecture by Henry Adams and Enrique Alvarado. Discover how real-valued functions on spaces can be used to create compact cellular models, reflecting important properties of the function. Learn about CW cell complexes, the Morse lemma, and the two main theorems of Morse theory. Delve into Morse complexes, Morse-Smale complexes, and techniques for simplifying Morse complexes. Gain insights into practical applications, including examples from material science and the use of software packages like the Topology Toolkit. From the basics of nudged elastic bands to the intricacies of Van der Waals potentials, this comprehensive introduction covers key concepts and their real-world relevance in applied algebraic topology.

Introduction
Outline
Moores theory
nudged elastic band
CW complexes
Morse functions
Moores lemma
Saddle points
Regular points
First Moores theorem
Second Moores theorem
Morse complex
Morse mail complex
Simplifying critical points
Software package example
Van der Waals potential
Material Science examples
Topology Toolkit
Conclusion