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I am researching spectral theory of differential operators and Schrödinger operators using methods from microlocal analysis and harmonic analysis. The Schrödinger operator corresponds to the energy of quantum mechanical systems, and by analyzing it via microlocal analysis, we can investigate the properties of its spectrum in connection with classical mechanical systems. Of particular interest is the spectral theory on Lorentz manifolds. In recent years, there have been intriguing developments in representation theory related to this topic, and applications to quantum field theory on curved spacetime have also been noted. However, there are many situations where existing tools cannot be applied, so it is necessary to develop new methods, which is one of the excitement of this topic. My other interest lies in the smoothing effects for time-dependent Schrödinger equations.