• Foam Rheology: Solution of problems relating to the flow of foams. Numerical implementation of meso-scopic bubble-scale models using the Surface Evolver, quantifying the role of viscosity in the flow of complex fluids such as foams.
• Foam Drainage: Use of analytical techniques, such as similarity solutions, and numerics to solve partial differential equations describing the viscous flow of liquid through a network of thin collapsible channels. Simple experiments on aqueous foams and soap films.
• Simulation of Cellular Structures: Analysis of instabilities in small clusters of cells. Simulation of area-minimizing structures using the Surface Evolver. Analysis and visualisation of three-dimensional disordered structures.
• Biological Morphology: Investigation of the morphology of echinoids (sea urchins) using an analogy with bubble formation. Application of the results of packing problems to infer details of the growth of biological systems such as flowers.
• Pressure Impulse Theory: Analysis of pressures induced by breaking waves on coastal structures. Potential theory.

Simon graduated with a degree in Applied Mathematics from the University of Warwick in 1994. His PhD research at the University of East Anglia explored the effects of the large pressures generated by breaking waves, for example when they impact against coastal structures. Simon then moved to Trinity College Dublin where he investigated the Physics of Foams. His foam research continued when he came to Aberystwyth in 2005, first as a lecturer, then reader, before being awarded a personal chair in 2010. He held an EPSRC Advanced Research Fellowship on foam structure and flow from 2006 to 2011, became a Fellow of the Learned Society of Wales in 2013, a Senior Fellow of the Higher Education Academy in 2016, and was head of the Department of Mathematics from 2014 to 2024.