  In this survey, we review some applications and extensions of the author's
results with Richard Melrose on propagation of singularities for solutions to
the wave equation on manifolds with conical singularities. These results mainly
concern: the local decay of energy on noncompact manifolds with diffractive
trapped orbits (joint work with Dean Baskin); singularities of the wave trace
created by diffractive closed geodesics (joint work with G. Austin Ford); and
the distribution of scattering resonances associated to such closed geodesics
(joint work with Luc Hillairet).
