Ian Short


Postdoc position in SL2-tilings

The Open University is recruiting a postdoctoral research associate to work on my EPSRC funded project The Farey framework for SL2-tilings. You can apply for it from the following link.

Postdoctoral Research Associate – The Farey framework for SL2-tilings

It starts on 1 July 2022 and lasts three years. Some background to the project can be found on the EPSRC project page


Additionally, the following paper gives some of the mathematics underpinning the project.


That paper explores SL2-tilings over the integers using the  Farey complex in the hyperbolic plane. Part of the project will involve Farey complexes for other rings, such as the Farey complexes for the four unital commutative rings of order four, shown below (click on the image for a clearer version).

I welcome queries!

My thanks to the EPSRC reviewers who supported the proposal making the project possible.

Rewilding Britain

I recommend this short video for the vision of Rewilding Britain.

Royal Institution Masterclass

Many thanks to those who attended today’s Royal Institution Masterclass on Navigating by numbers, which I hosted together with Margaret Stanier. The desmos activities will remain active for a couple of weeks yet, available at


Here are the slides from the masterclass.

Navigating by numbers presentation first page

Maths Week Scotland

Thank you to those who joined Andrew and me tonight for the Navigating by numbers online workshop as part of Maths Week Scotland. Here’s the abstract for the workshop:

Our exploration will take us from intriguing frieze patterns of numbers, through triangulated polygons and repeated fractions, to a beautiful infinite tessellation with remarkable properties. Along the way we will meet the mathematicians who forged this path of discovery, and we will get a taste of deeper aspects of the subject.

And here’s a recording of the workshop itself:

The mathematics of dessins d’enfants

I had the pleasure today of delivering a workshop in Belfast on The mathematics of dessins d’enfants as part of the Northern Ireland Science Festival 2020. This workshop explored some of the more geometric aspects of the Navigating by Numbers outreach programme. The abstract sums it up:

The workshop will be an interactive exploration of the incredible mathematical theory of dessins d’enfants (“children’s drawings”). We can think of a dessin d’enfant as a shape that you obtain by gluing together a number of triangles. Remarkably, these simple objects give rise to far deeper mathematical ideas, which form an active subject of modern research. With models and illustrations, and hands-on activities, the workshop will explore some of the secrets of dessins d’enfants, and look at the mathematicians who have developed the subject.

The workshop is for those with appreciation of shape and symmetry. By exploring models and pictures, participants will appreciate the flavour of an exciting branch of contemporary mathematics. We will meet some beautiful geometric ideas, which will be a source of inspiration for aspiring mathematicians and artists alike!

Travelling to Belfast was an epic and thoroughly enjoyable trip. I don’t fly on aeroplanes – instead I caught a train from Milton Keynes to Holyhead, then a ferry from Holyhead to Dublin, and a train from Dublin to Belfast. I felt nostalgic for the familiar dump that surrounds Dublin Connolly Station. I used to live in Dublin, and took salsa classes near the station.

Many thanks to the creative, intelligent attendees of the workshop, of all ages, for a thoroughly enjoyable experience.

Image of the Farey tessellation with two adjacent triangles highlighted

Screenshot of a slide from the workshop

Navigating by numbers

Today marks the launch of the Navigating by numbers outreach programme. The purpose of this programme is to communicate an attractive array of mathematical ideas centred on the Farey graph to as wide an audience as possible – from school learners to academic researchers.

My PhD student Margaret Stanier and I launched the programme with an interactive display at Maths Fest 2020, featuring origami, papier mâché, and my daughters’ Geomag.

Navigating by numbers poster

Poster on Farey graphs from the workshop

International Rebellion

Extinction Rebellion’s International Rebellion begins today in London. Please support them! I will join them later in the week.

The environmental collapse of the Earth is summed up well by the first lines of David Wallace-Wells The Uninhabitable Earth:

It is worse, much worse, than you think. The slowness of climate change is a fairy tale, perhaps as pernicious as the one that says it isn’t happening at all…

You can support Extinction Rebellion financially too. E and I donated £500 and then committed to £60 per month.

Swifts return

Swifts returned to Woburn Sands today, just two so far. One house martin flying around as well.

Wilding, by Isabella Tree

This is a wonderful, inspiring book of wilding at the Knepp Estate in West Sussex. The author and her husband own a few thousand of acres of land around Knepp Castle, which until twenty years ago was heavily farmed. In the early 2000s, however, they began giving up parts of the land to wildlife. Following the example of successful wilding projects in the Netherlands, they applied a policy of minimal intervention, introducing some select large herbivores and leaving them to it (subject to legal restraints and various other complications).

The results have been astounding.

Today the land is a haven for a huge variety of wildlife, plants and animals. A few highlights are purple emperor butterflies, turtle doves, nightingales, 13 bat species, and all 5 of the UK’s owl species. The story demonstrates the richness of life that we could have in this country if we stopped farming so intensively, cutting, burning, spraying with deadly chemicals, building on ancient woodland, removing scrub, and tidying the countryside.

Towards the end the author quotes the American conservationist Aldo Leopold, who wrote almost a century ago: ‘One of the penalties of an ecological education is that one lives alone in a world of wounds.’ I encourage you to read this book, learn a little ecology, and help to bring life back to this sorely damaged country. And join Rewilding Britain!


UK-wide climate emergency

Caroline Lucas (MP for the Green Party) tabled a motion to the UK parliament on the 13 March to recognise that the world has a climate emergency. The motion proposes that the government introduces a new green deal to radically reduce the production of greenhouse gases. The motion is here –

UK-wide climate emergency.

It has been signed by politicians from across the political spectrum. You can

write to your MP

to encourage her or him to sign the motion. I wrote to Nadine Dorries; she has yet to sign up to it.

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