Last spring, we presented Spectral Variational Integrators, a
class of variational integrators that had both excellent conservation
properties and exhibited geometric convergence. This talk will present
extensions to this work, including Spectral Variational Integrators on
lie groups, pseudospectral variational integration of the one
dimensional wave equation, and several conjectures about the behavior
of Spectral Variational Integrators based on observations of numerical
examples.