The terms “analysis” and "Partial Differential Equations (PDE)" are extremely wide, including a rich variety of areas in both pure and applied math. They further make connections to such neighboring areas as statistics, physics and engineering. Subareas: real analysis, complex analysis, functional analysis, operators in Hilbert space, operator algebras, harmonic analysis, measure theory, machine learning, differential equations (including PDEs), numerical analysis, dynamical systems, and approximation theory.