Who are we and what do we do?
We are a research group led by David Sumpter and based in the mathematics department of Uppsala University. Our research is about understanding collective behaviour in biological and social systems.
What is research in collective behaviour?
Research in collective behaviour is about linking together the way we understand systems at different levels. Take a bird flock as an example. Here we see many individuals moving in unison, but there is no clear leader or global controller. The question is how the bird's interactions link together to produce the overall motion of the flock. Similar questions arise when we look at ant and bee colonies, cellular interactions, and the human economy. How do individual behaviours integrate to produce global dynamics?
Why is understanding collective behaviour important?
We live in a data rich world. We can use image analysis to track the motion of fish and GPS to track birds. There are vast databases of information about the social welfare and economic development of humans. We can measure the flow of nutrients within a microorganism. But the question is how we understand this data? How is all this individual behaviour, be it of animals, humans or cells, integrated to produce dynamics at the level of the group? These are unanswered and general questions which research on collective behaviour addresses.
What has this got to do with mathematics?
Mathematics is a rigorous way of reasoning about the world. It is also a way of reasoning which allows us to draw powerful analogies between different systems. We use a range of statistical, mathematical and computer simulation tools to quantify and then model the behaviour of groups. These tools include differential equations, stochastic models, self-propelled particle models and individual-based models.