Seminar in the Analysis and Methods of PDE - Christopher K.R.T. Jones

Explore the stability of nonlinear waves and patterns in a seminar presented by Christopher K.R.T. Jones from the University of North Carolina at Chapel Hill. Delve into the analysis of steady states in nonlinear partial differential equations, focusing on stability indices determined by unstable eigenvalue counts. Examine two key approaches: the Evans Function and the Maslov Index, understanding their geometric foundations and applications to eigenvalue equations. Compare the strengths and limitations of these methods, particularly the Maslov Index's more stringent requirements. Discover recent advancements that have expanded the applicability of both theories to increasingly complex problems beyond their original scope.