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PDEs, created to describe the mechanical behavior of objects such as vibrating strings and blowing winds, has developed into a subject that interacts with many branches of mathematics, such as differential geometry, complex analysis, and representation theory. Modern techniques in the analysis of PDEs include harmonic analysis, functional analysis, microlocal analysis, topological methods, and symplectic geometry, to name a few. Members of our PDE group are active in studies of linear and nonlinear wave motion, spectral theory and scattering theory, analysis on singular spaces, and inverse problems.