Chance, luck, and ignorance; how to put our uncertainty into numbers We all have to live with uncertainty about what is going to happen, what has happened, and why things turned out how they did. We attribute good and bad events as ‘due to chance’, label people as ‘lucky’, and (sometimes) admit our ignorance. I will show how to use the […]
Perfect sampling, old and new The possibility of obtaining perfect samples efficiently from a complex probability distribution entered the consciousness of the community in the mid-nineties with the invention of `coupling from the past’ by Propp and Wilson. The study of perfect samplers of course has considerable theoretical appeal. But, in addition, their ‘self clocking’ aspect may have practical advantages. […]
The emergence of hydrodynamics in many-body systems One of the most important problems of modern science is that of emergence. How do laws of motion emerge at large scales of space and time, from much different laws at small scales? Hydrodynamics offers a basic but very relevant example. Molecules in air simply go along their journey following Newton’s equations. But […]
Category Theory in Epidemiology “Stock and flow diagrams” are widely used for modeling in epidemiology. Modelers often regard these diagrams as an informal step toward a mathematically rigorous formulation of a model in terms of ordinary differential equations. However, these diagrams have a precise syntax, which can be explicated using category theory. Although commercial tools already exist for drawing these […]
Navigating the Unknown: Harnessing Uncertainty in Renewable Energy and Heart Health Uncertainty Quantification (UQ) emerges as a guiding force in the turbulent sea of data-driven domains, from energy to health. This talk presents a methodology that harnesses UQ for robust renewable energy forecasting, employing a stochastic differential equation model that sails beyond the challenges of wind and solar predictability. Shifting […]
Pattern Formation Through Spatial Segregation
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 […]