The department has a wide variety of research interests, and has collaboration with many institutions both locally (Universities of Stellenbosch, Cape Town, KwaZulu-Natal, Free State, African Institute of Mathematical Sciences, Durban University of Technology) and internationally (Russia, UK, India, Iran, Slovakia). There are several postgraduate students being supervised within the department.
In the area of general relativity, relativistic astrophysics and cosmology, the department is working on a project in dark energy. The universe is currently believed to be expanding, but it was thought for a long time that this expansion was decelerating. However, observational evidence emerged in the late 1990’s that this expansion is actually accelerating. To explain this acceleration, one requires the universe to have around 70% more “matter” than was thought previously. This still mysterious form of “matter” is called dark energy, and it is one of the major unsolved problems of modern cosmology to explain the source and nature of this dark energy, as well as to come up with suitable models for it. Together with local and international scientists, the department is trying to understand this dark energy.
Research areas in the department in mathematics include the theory of differential equations, Lie groups and Lie algebras, Riemannian geometry, theory of distributions and invariance principles in initial value problems, symmetry in mathematical modelling, theory of approximate transformation groups and perturbation methods in group analysis.
In applied mathematics the research areas are symmetry, conservation laws and group invariant solutions in fluid dynamics, group theory in turbulence, Lie symmetry analysis, analytical integration and solution of initial value problems for mathematical models in finance, mathematical image processing, climate modelling, applied and computational mathematics including, mathematical optimization, multiobjective optimization, multilevel optimization, metaheuristic, matheuristic, hyperheuristic, operations research, modeling and simulation, modelling population and disease dynamics, statistical, mathematical modelling and analysis of infectious disease processes, biostatistics and epidemiology
In statistics signal processing, multiscale analysis, climate modelling, process monitoring and fault diagnosis, statistical quality control, Probability Theory, and Stochastic Processes, applied statistics, statistical machine learning and smart grid modelling. Research in the biological and health sciences particularly modelling population and disease dynamics, statistical and mathematical modelling and analysis of infectious disease processes at the individual and population level, biostatistics and epidemiology such as the analysis of survival analysis, Spatio-temporal and the Bayesian survival approach, is also carried out.
Some staff members are currently registered for masters/doctoral degrees.