Many applications require the solution of time-dependent
partial differential equations (PDEs) on surfaces or more general
manifolds. Methods for treating such problems include surface
parameterization, methods on triangulated surfaces and embedding
techniques. This talk considers an embedding approach based on the
closest point representation of the surface which is very general with
respect to the underlying surface and PDE, yet is extremely simple.
Recent applications to high-order PDEs and Laplace-Beltrami
eigenmodes are given to illustrate the approach.