My research interests are based on the idea of classical-quantum correspondence. Differential geometry describes a classical system, such as Newtonian Mechanics, geodesic flow. The classical system tells us how the related quantum system, such as drum vibrations, quantum particle distribution, should behave. The machinery used to make this connection is called microlocal analysis, which means we study solutions of Partial Differential Equations living in a classical phase space, varying both in position and frequency of oscillation. I am mostly interested in chaotic and singular classical systems, which lead to quantum systems exhibiting equidistribution of waves or unstable scattering.