Microlocal analysis and global analysis of dispersive equations

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We studied the relation between properties of solutions (in particular, singularities of solutions) to linear dispersive equations and geometry of symbols of the equations. As a model we considered propagation of singularities of solutionsto Schrodinger equations with perturbed quadratic potentials and obtained a necessary and sufficient condition for the wavefront sets of the fundamental solutions to be invariant under some class of potential perturbations. We also obtained results on growth order of solutions to wave equations with spatially compact metric perturbations (joint work with T.Nishitani and H.Ueda).