The group in analysis does research in diverse areas of analysis from pure to applied; modern and classical: analytic number theory, partial differential equations (PDE) , dynamical systems, linear and non-linear, stochastic analysis, functional analysis, harmonic analysis, commutative and non-commutative, Fourier analysis, abstract and computational, wavelets,  and operator algebras.  There are applications are to physics, biology, engineering (e.g., signal/image processing); statistics, actuarial science, biostatistics, economics, business, and finance.