Analysis is the study of functions, continuity and discontinuity, the infinite and the infinitesimal. At McMaster research in analysis deals with Harmonic Analysis and Partial Differential Equations. Harmonic analysis traces its roots back to Fourier series and is key for image segmentation, pattern recognition, and data compression. Current research involves oscillatory integrals, moment problems, and wavelets. Research in Partial Differential Equations includes fully nonlinear equations, free boundary problems, geometrical PDEs, degenerate elliptic and parabolic systems, and small divisor problems.