Timothy Paczynski

Morse theory is the study of differentiable functions on objects called manifolds which locally look like copies of Euclidean space. Insights from Morse, Cayley, and Maxwell
about these functions were originally used in the study of geodesics, and topography. This talk won’t go into these applications but after a brief survey of manifolds we will introduce critical points of manifolds and a class of functions with nice critical points called Morse functions. From here we will discuss how critical points and Morse functions allow us to determine how to decompose manifolds into pieces that are continuous deformations of their original parts. Finally, to see how one might use such a seemingly abstract tool, it will be shown that any manifold which admits a particular type of Morse function must be homeomorphic to a sphere.

Zoom link: https://wwu-edu.zoom.us/j/92041720377?pwd=QW9aUWFKZGM5WWtGRjF2N2NTOTExUT09

Meeting ID: 920 4172 0377

Passcode: Pandemic