In many natural systems, such as the climate, the flow of fluids, but also in the motion of certain celestial objects, we observe complicated, irregular, seemingly random behaviours. These are often created by simple deterministic rules, and not by some vast complexity of the system or its inherent randomness. A typical feature of such chaotic systems is the high sensitivity of trajectories to the initial condition, which is also known in popular culture as the butterfly effect.

Oxford Mathematician Vidit Nanda talks about his and colleagues Harald Oberhauser and Ilya Chevyrev's recent work combining algebraic topology and stochastic analysis for statistical inference from complex nonlinear datasets.

"It is not difficult to generate very complicated dynamics via very simple equations. Consider, for each parameter r > 0 and natural number n, the update rules

Oxford University is committed to encouraging as wide a range of applicants as possible. Oxford Mathematics is part of that commitment. But what does that mean in practice? Well over the Summer months it means UNIQ, Oxford’s way of breaking down barriers and building bridges. A kind of construction work for the mind.