I am an assistant professor in the Department of Mathematical Sciences at Durham University. I develop computational, mathematical techniques to investigate complex, weirdly-behaving fluids and biological phenomena.
I also give popular maths lectures for all ages across the UK, most commonly on the maths of chocolate fountains. I write and help produce the maths magazine Chalkdust; and I also teach courses for postgraduates, undergraduates and A-level students.
Research
My research is in developing mathematical and computational techniques to investigate complex fluids. These are fluids that don’t behave in the way that we would expect more standard Newtonian fluids (like water, air and honey) to. So this might include mayonnaise, blood or chocolate.
This behaviour is often due to complex microscopic structure. The mathematical methods I develop, in conjunction with high-performance computing, allow me to carefully model this structure and then create very large simulations, providing a clearer picture of the fluid’s overall behaviour.
Often in biology and industry, these fluids have objects and organisms moving through them: for example, I have investigated sperm swimming through mucus. Such organisms are particularly interesting as they create and break microstructure as they move, which can dramatically alter the properties of the fluid.
I am also interested in using powerful but accessible web technology to solve scientific problems and present them to the world. Check out VisualPDE.com, where you can solve nonlinear PDEs interactively in real time, in your browser or on your phone.
Details of my interests and links to my GitHub repositories are on the research page.
Popular maths and outreach
I give maths outreach talks at school enrichment days and general public events regularly. In doing so, I have worked with the Royal Institution, the BBC, and the Science Museum.
I co-founded the popular maths magazine Chalkdust in 2015. We now print 4000 copies per issue and distribute to universities and individuals all over the world. I have written a number of articles as me and as the local agony uncle.
Teaching
I currently teach fluid mechanics to third-year undergraduates at Durham. Before that, I taught the mathematical biology course. At Imperial College and during the pandemic, I taught postgraduate research computing courses. I spent three years teaching an undergraduate calculus course which I wrote at UCL for the BASc programme, and I spent five years teaching A-level further maths for the Advanced Maths Support Programme. From time to time I do some private tutoring.
and…
I work with St John Ambulance on a volunteer basis, helping to run summer camps and developing large online systems for their training and youth programmes.
Additionally, I have taken on professional web development work, designing administrative systems, and have worked on a number of interesting projects, including a system for the prison service.