Drawing motivation from the theory of dynamical systems, traveling waves can be viewed as fixed points of a flow on an infinite dimensional manifold. As such, the eigenvalue problem associated with linearizing about the traveling wave is often reduced to a boundary value problem of a linear non-autonomous ordinary differential equation on the line. In such problems, one can use the geometry of vector bundles and the Grassmannian to recast the original (temporal) spectral problem as a geometric condition. I plan to talk about a couple of examples of how this technique has been applied, first with some scalar-valued partial differential equations and then, if time permits, with systems. Speaker(s): Robby Marangell (Sydney University)