Speaker: Margaret Beck
Title: Spectral stability and spatial dynamics in partial differential equations
Abstract: Understanding the spectral stability of solutions to partial differential equations is an important step in predicting long-time dynamics. Recently, it has been shown that a topological invariant known as the Maslov Index can play an important role in determining spectral stability for systems that have a symplectic structure. Moreover, this perspective has lead to a framework for developing a spatial dynamics in multiple spatial dimensions. In this talk, the notions of spectral stability, the Maslov Index, and multidimensional spatial dynamics will be introduced and an overview of recent results will be given.