The research interests of the Department cut a broad swathe through both pure and applied areas of mathematics, ranging from analysis, nonlinear partial differential equations, ergodic theory, and geometry to quantum field theory, general relativity, string theory, fluid dynamics, complex systems, mathematical biology, statistics, and modelling in the life sciences. A particular emphasis is placed on research at the interface between pure and applied mathematics. Research in the Department is organised into a number of research groups, but there are many overlaps and links between these: