Abstract for Margaret Beck

Margaret Beck (Boston University)

Thursday, March 30, 2023

Determining spectral stability via the Maslov index and conjugate points

Abstract: Being able to determine the spectral stability of stationary solutions is an important step towards understanding the long-time behavior of PDEs that describe a variety of physical and biological processes. For systems whose evolution respects certain symplectic structures, spectral stability can be understood through the use of a topological invariant know as the Maslov index and the counting of what are called conjugate points. In this talk, these structures and tools will be defined and described, and recent related results will be presented that allow one to efficiently and rigorously determine spectral stability via validated numerics for reaction-diffusion systems with gradient nonlinearity and for the Swift-Hohenberg equation.