Outreach

Maths enrichment in the East Midlands

My EPSRC research fellowship generously allows me to spend part of my time on outreach activities. If you’d like me speak at your school or event, please get in touch.

I also deliver maths sessions for on-campus events such as Inspiring Minds: STEM. If you’re a teacher wanting to arrange a campus visit at Loughborough, please contact the School and College Liaison.

Some topics I enjoy doing sessions on are:

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  Athletics track geometry. In this session we aim to give a mathematically precise description of an athletics track. We discuss its shape and how the start lines should be staggered to ensure a fair race. After we have done this for the standard track layout, the pupils will get some time to design their own track and compute its length and the appropriate stagger of the start lines.

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  The mathematics behind the rainbow. A mathematical problem-solving journey to explain how a rainbow forms. We start with a few puzzles involving a farmer and an injured cow, which are secretly a review of (or introduction to, if appropriate) reflection and refraction. With these tools in hand, we look at the geometry of the rainbow, focusing on what happens to a ray of light within a spherical raindrop.
  (See also the lovely summary of this lecture, published by Oakham School after I delivered it there.)

Videos

You can visit my YouTube channel or browse the pages below for some additional information alongside the videos:

Waves, not cars – modelling traffic as a fluid

We give a visual introduction to the Lighthill-Whitham-Richards model of traffic flow and the method of characteristics. Through this model, we study examples of light and heavy motorway traffic, traffic lights, and the use of variable speed limits ...

Iterations and chaos

A two-part video on iterations and chaos. The first part reviews some textbook material on the concept of iterations and how to visualise them. The second part has the more ambitious goals of understanding the titular claim of a 1975 paper by Tien-Yien Li and James A Yorke: period three implies chaos ...

The shapes of waves of ships and ducks

A video about the pattern of waves making up the wake of a ship or a duck. This is a common topic in university-level fluid mechanics courses, but my intention was to give a fairly complete explanation without assuming any more advanced knowledge than trigonometry ...

Rainbows don’t work the way you think they work

This video on the mathematics behind rainbows communicates visually (without formulas) how the full story is more complicated, but also more beautiful, than "different wavelengths reflect at different angles" ...

Blog posts

If you want to get an idea about my research area, have a look at blog posts below. There is a lot of maths between what is taught in school and the highly specialised topics of today’s research. In fact, these intermediate levels contain some exciting insights that aren’t too difficult to explain:

Waves of predators

In mathematical biology, one of the simplest models of population dynamics is the Lotka-Volterra model. It is a system of two differential equations, modelling the interaction of the populations of two species: a predator and a prey. The mathematics behind it has a surprising connection to the dynamics of waves in a shallow canal ...

Four different dynamical systems

This multimedia post features four different dynamical systems to illustrate some properties of that relevant to my research: we'll talk about the difference between "integrable" and "chaotic" dynamical systems, and the difference between "continuous-time" and "discrete-time" dynamical systems ...

What is… a variational principle?

Variational principles play fundamental role in much of mathematical physics and are a key topic in my own research. That's a lot to cover, so let's start with a little story ...

What is… an integrable system?

The oversimplified answer is that integrable systems are equations with a lot of structure. The kind of equations we are thinking about are differential equations, which describe change. Whenever something is moving, you can count on it that physicists would like to describe it using differential equations ...

In print

Chalkdust is a “magazine for the mathematically curious”.

I wrote an article on Hamiltonian mechanics and Noether’s theorem for issue 15 and an article on involutes for issue 22.

Online events

In October 2022 I appeared in a 24-hour maths game show, with a 30 minute segment on a 1-dimensional version of Conway’s Game of Life. You can still watch the recording and play with copy of the google spreadsheet.

In May 2025 I contributed a segment the 5th Clopen Mic Night, asking the slightly absurd question “what if everything in the universe suddenly started shrinking?”