The Other Pure Seminar (TOPS): Prolongation and symmetry (1 of 2)

Speaker: Mike Eastwood

Title: Prolongation and symmetry

Abstract: The derivative of a vector field on flat Euclidean n-space may be viewed as a function with values in the nxn matrices. This matrix may be broken into pieces (symmetric part, skew part, trace, and so on) and we can set some parts to be zero to impose various natural PDE on the original vector field. Prolongation is a technique that allows us to investigate and sometimes solve these PDE, often with a geometric interpretation in terms of symmetries. I’ll start from scratch and use a whiteboard but you can find rough notes in the form of slides linked from here

https://sites.google.com/view/geilo2025-geometric-analysis/titles-and-abstracts