The underlying theme of the group is the application of rigorous mathematical models to quantitatively analyse and understand in depth problems in science and engineering. We have a wide range of mathematical expertise and techniques in modelling, from partial differential equations, to agent modelling, dynamical systems, or topological methods. Often, the research take place in close interdisciplinary collaborations. As an example, we have developed a very successful model of lithium-ion batteries by combining classical differential equation modelling with asymptotic analysis and state of the art coding to produce a software package that is both fast and comprehensive. Other examples are the application of asymptotic analysis in controlling aircraft sounds, stochastic methods in modelling gene expression and agent-based techniques in healthcare. We apply topological data analysis to model phase transitions of mesoscopic physical systems, and to enhance and up-scale optical imaging in medical applications, as precursors to efficient machine learning and data analysis.