Graduate Student Seminar I William Bell, Pseudospectra and Dynamics

Microsoft Teams Meeting (AMATH-Grad Students)

Speaker

William Bell | Applied Math, University of Waterloo

Title

Pseudospectra and Dynamics

Abstract

This talk will present a basic explanation of pseudospectra, a tool from the perturbation theory of eigenvalues. It is well-known that eigenvalue methods are a handy tool for answering many questions in the study of the asymptotic and local behaviour of dynamical systems. However for many questions, eigenvalue methods fail. In these cases, pseudospectra offer many tools for extending eigenvalue analysis. For instance, transient behaviour is more usefully described by the pseudospectrum than by eigenvalue behaviour. The pseudospectrum also offers insight about when and why eigenvalue methods fail. 

We will proceed by introducing exactly what the pseudospectrum is, introducing useful tools for computations, and explaining simple results that can be used by anyone to study the pseudospectrum, namely the Kreiss Matrix Theorems.