Our analysis research group is one of the UK’s top centres for research in the field, especially in linear and nonlinear PDEs and harmonic analysis. Your passion for mathematical analysis will be rewarded by contact with, and supervision by, world-leading academic staff, a rich seminar and working group programme and ultimately a qualification that boasts an internationally respected pedigree. The School of Mathematics is a vibrant community of more than 60 academic and related staff supervising 60 students. We have a unique focus on the interplay of classical Euclidean harmonic analysis with the modern theory of PDEs. We study harmonic analytic ideas in number theory, geometric measure theory, combinatorics, and discrete geometry and geometrically invariant inequalities; and we investigate applications of harmonic analysis to elliptic and parabolic PDEs with rough coefficients and/or on rough domains. We also study: * nonlinear hyperbolic, dispersive and kinetic equations and systems arising in the classical field theories of mathematical physics, mathematical biology and, in connection with black holes, mathematical general relativity * free-boundary problems, optimal mass transportation and Monge-Ampère equations in nonlinear elasticity and other continuum theories * well-posedness for supercritical initial value problems with noisy initial data