Title: Modulational and Subharmonic Dynamics of Periodic Waves

Abstract: In this talk, we will explore some of the modern techniques used to study the stability and dynamics of periodic solutions to nonlinear partial differential equations (PDEs) arising from applications. We will develop some of the intuition for these techniques using ordinary differential equations (ODEs) and integral transforms. This intuition will then allow us to investigate the stability and dynamics of several PDEs when subjected to various types of perturbations.