Research Teach Repeat: Pure Mathematics

Pure mathematics involves the development of new, cutting-edge, mathematical theory, some of which may be aimed at solving specific problems, with other parts motivated purely by the intrinsic beauty of the mathematics itself. In some cases, the mathematical theory developed is intimately connected to our understanding of the world, and universe around us. Our novel work in pure mathematics includes the study of partial differential equation models with free boundaries – such models are high relevant for studying the dynamics of populations that are in competition, invasive species, the spread of disease connected to moving populations and a number of other applications. We have a strong core of researchers that work in differential geometry; as well as being a rich topic for mathematical research in its own right, this area provides the necessary theory for mathematical physics, including the understanding of general relativity, black holes and string theory. In recent work, we have developed new theory in the study of economic games via catastrophe theory, and exploited our knowledge of topology in data analysis. Other ongoing research interests include category theory, and the theory of C* algebras.