I thought to see the fairies in the fields, but I saw only the evil elephants with their black backs. Woe! How that sight awed me! The elves danced all around and about while I heard voices calling clearly.... Puzzled? Curious? Come and join in the chase for the key to this cipher message, learn about the beautiful mathematics underlying the ancient art of ringing the changes, and find out what all this has to do with juggling.

Many interesting natural phenomena are hard to predict. When modelled as a dynamical system, this unpredictability is often the result of rapid separation of nearby trajectories. Viewing the dynamics as acting on a probability measure, the mixing property states that two measurements (or random variables), evaluated at increasingly separated times, become independent in the time-separation limit. Thus, the later measurement becomes increasingly difficult to predict, given the outcome of the earlier measurement. If this approach to independence occurs exponentially quickly in time, one can profitably use linear operator tools to analyse the dynamics. I will give an overview of these techniques and show how they can be applied to answer mathematical questions, describe observed behaviour in fluid mixing, and analyse models of the ocean and atmosphere.

Space and time together constitute one of the most basic elements of physical reality. Since Einstein spacetime has become an active participant in the dynamics of the gravitational force. However, our notion of a quantum spacetime is still rudimentary. String theory, building upon hints provided from the physics of black holes, seems to be suggesting a very novel, "holographic" picture of what quantum spacetime might be. This relies on some very surprising connections of gravity with quantum field theories (which provide the framework for the description of the other fundamental interactions of nature). In this talk, I will try and convey some of the flavour of these connections as well as its significance.

Electricity demand forecasting plays an important role in short-term load allocation and long-term planning for future generation facilities and transmission augmentation. Planners must adopt a probabilistic view of potential peak demand levels, therefore density forecasts (providing estimates of the full probability distributions of the possible future values of the demand) are more helpful than point forecasts, and are necessary for utilities to evaluate and hedge the financial risk accrued by demand variability and forecasting uncertainty. Electricity demand in a given season is subject to a range of uncertainties, including underlying population growth, changing technology, economic conditions, prevailing weather conditions (and the timing of those conditions), as well as the general randomness inherent in individual usage. It is also subject to some known calendar effects due to the time of day, day of week, time of year, and public holidays. I will describe a comprehensive forecasting solution designed to take all the available information into account, and to provide forecast distributions from a few hours ahead to a few decades ahead. We use semi-parametric additive models to estimate the relationships between demand and the covariates, including temperatures, calendar effects and some demographic and economic variables. Then we forecast the demand distributions using a mixture of temperature simulation, assumed future economic scenarios, and residual bootstrapping. The temperature simulation is implemented through a new seasonal bootstrapping method with variable blocks. The model is being used by the state energy market operators and some electricity supply companies to forecast the probability distribution of electricity demand in various regions of Australia. It also underpinned the Victorian Vision 2030 energy strategy.

The term "overlapping" refers to a certain fairly simple type of piecewise continuous function from the unit interval to itself and also to a fairly simple type of iterated function system (IFS) on the unit interval. A correspondence between these two classes of objects is used to: 1. find a necessary and sufficient condition for a fractal transformation from the attractor of one overlapping IFS to the attractor of another overlapping IFS to be a homeomorphism and 2. find a formula for the topological entropy of the dynamical system associated with an overlapping function. These results suggest a new method for analysing clocks, weather systems and prime numbers.