• How do you help an NHS 111 call-responder know, during a call from a member of the public, whether their conversation with that person is going well or badly?
  • How do you demonstrate the economic difference that would arise if construction projects at Heathrow airport were planned rather than arranged piecemeal as they crop up?
  • When crisps are being cooked in oil, the water content vaporizes and the resulting buoyancy causes them to come unstuck from the metal mesh and float up, but what determines exactly when this happens?
  • And further down the crisp production line when they slide down a short chute, how do you design its shape to make the crisps come out consistently aligned on the conveyor belt so that they will stack properly?
  • If you want to make aircraft wing components from carbon fibre mats by folding without cutting, with a bound on the angle-changes between the sets of fibres, how does that constrain the geometry of the resulting wing and spar shapes?
  • When crops are grown hydroponically in a long tube, how do you control the flow of water, air and nutrients to give the plants the best growing conditions along the whole length of the tube, right from the start through to maturity when their roots fill a substantial part of the cross-section?
  • If computer processing of departure lounge images is used to count people in an airport, how do you prove the accuracy of the system when there is so much more variability in the results of manual counting of people in the images?
  • When testing chemicals for potential use as herbicides, it is usual to do some experiments on a few thousand chemicals, pick a few hundred of them for some more costly experiments, then a few dozen of those for still more costly experiments, and finally a handful for field trials. But why? — how should you decide how many to take forward from one stage to the next? How should you combine results from different stages? How many stages should you have anyway?

These — too briefly — were the problems that were addressed at the 2018 UK Maths-in-Industry Study Group held at the University of Bath from 16–20 July.

2018 UK Maths-in-Industry Study Group

Around 80 mathematicians from UK and overseas universities worked on these problems alongside the scientists from the participating companies to generate ideas, mathematical models, analysis, computation, visualization and new experiments that all helped shed light on these questions and begin to answer them. It is a no-holds-barred activity, with everyone working and contributing their ideas, from PhD students to senior professors. It also draws on the whole of mathematics, so during the week we used Stefan problems, extreme value statistics, the shallow water equations, differential geometry, Darcy flow, quaternions, Bessel functions, Markov decision processes, machine learning, optimal stopping problems, Bayesian updating, homogenisation, asymptotics, experiments via videoconference and much more besides.

And how did the industrial scientists view the outcomes presented on the final morning of the meeting?

I’m very impressed — it’s been very interesting, good fun and good to have different takes on it. Some of this will be very challenging to people who think about the problem in a static way.

It’s really amazing. I’m very impressed with the collective work.

Thank you very much. It’s been very illuminating and very good to be able to describe and illustrate the shapes.

Very impressed. You managed to cover a lot of ground in a week and the director was very impressed too. It’s definitely going to be useful and it was very impressive to see the graphics.

A massive massive thank you — we brought a whole host of issues and it’s an unbelievable amount of work.

It’s fascinating. There’s a lot of food for thought, and potentially big savings. Nobody has ever looked at the data this way before.

Let’s face it — it’s like opening Christmas presents.

The Smith Institute has more than fifteen years’ experience in supporting the annual UK European Study Group with Industry. If you would like further information about Study Groups and how to participate or have any questions, please contact Judy Reynolds.