From Order to Chaos and Chaos to Order in Fluid Flows The eleven year solar activity cycle is a remarkable example of regular behaviour emerging from an extremely turbulent system. The jets on Jupiter sit unmoving on a sea of turbulent eddies. Astrophysical phenomena often display organisation on spatial and temporal scales much larger than the turbulent processes that drive […]
Finite Shadows of Infinite Groups, Finiteness Properties, and Geometry There are many situations in geometry and group theory where it is natural, convenient or necessary to explore infinite groups via their actions on finite objects. But how much understanding can one really gain about an infinite group by examining its finite images? Sometimes little, sometimes a lot. In this colloquium […]
Data Augmentation and Imagination The technique of data augmentation, whereby observed data are effectively augmented by additional quantities not actually observed in an experiment, has proved to be extremely powerful in modern statistics generally, and in Bayesian parametric inference in particular. This talk will describe its application to Bayesian inference for epidemic models where many challenges arise from the typically incomplete observations of epidemic processes.
Artistic Mathematics: Truth and Beauty This is about Henry’s work in mathematical visualisation: making accurate, effective, and beautiful pictures, models, and experiences of mathematical concepts. He discusses what it is that makes a visualisation compelling, and show many examples in the medium of 3D printing, as well as some work in virtual reality and spherical video. He also discusses his experiences […]
Postcards from Network Theory I will show some postcards of the use of network theory for solving real-world problems. After a very brief introduction I will start by illustrating such postcards. The postcard 1 is about the study of protein-protein interaction (PPI) networks. The postcard 2 is about the use of networks to describe the 3-dimensional structure of biomacromolecules. In particular, I will develop the concept of network communicability and […]
Mathematical Modelling of the Sleep-wake Cycle: Light, Clocks and Societal Rhythms We’re all familiar with sleep, but how can we mathematically model it? And what determines how long and when we sleep? In this talk I’ll introduce the non-smooth coupled oscillator systems that form the basis of current models of sleep-wake regulation and discuss their dynamical behaviour. I will describe how we have used models to inform debates on societal questions such as whether to move school start time […]
A Fluid Mechanic’s Analysis of Tea-cup Singularity One of the most fundamental issues in fluid dynamics is whether or not an initially smooth fluid flow can evolve over time to arrive at a singularity — a state for which the classical equations of fluid mechanics break down and the flow field no longer makes physical sense. While proof remains an […]
Ergodic Theory Without Invariant Measures Ergodic theory deals with dynamical systems from a measurable point of view. One considers transformations of a probability space, like the rotation of a circle over a typically irrational angle. In general, one considers transformations that may or may not preserve the given probability measure, but that will always preserve sets of measure zero. Iterating […]
Approximating Real Numbers by Fractions How well can you approximate real numbers by rationals with denominators coming from a given set? Although this old question has applications in many areas, in general this question seems impossibly hard – we don’t even know whether e+pi is rational or not! If you allow for a tiny number of bad exceptions, then a beautiful […]