This is an introduction to the article 

A. Beilinson, p-adic periods and derived de Rham cohomology, J. Amer. Math. Soc. 25 (2012), no. 3, 715--738.

Over the years, nonlinear and nonparametric models have attracted a great deal of attention. This is mainly due to the fact that most time series arising from the real-world exhibit nonlinear behavior, whereas nonparametric models, in principle, do not make strong prior assumptions about the true functional form of the underlying data generating process.

In this workshop, we will focus on the use of nonlinear and nonparametric modelling approaches for time series forecasting, and discuss the need and implications of accurate forecasts for informed policy and decision-making. Crucially, we will discuss some of the major challenges (and potential solutions) in probabilistic time series forecasting, with emphasis on: (1) Modelling in the presence of regime shifts, (2) Effect of model over-fitting on out-of-sample forecast accuracy, and, (3) Importance of using naïve benchmarks and different performance scores for model comparison. We will discuss the applications of different modelling approaches for: Macroeconomics (US GNP), Energy (electricity consumption recorded via smart meters), and Healthcare (remote detection of disease symptoms).

This talk will be a geophysicist's view on the emerging properties of a numerical model representing the Earth's climate and volcanic activity over the past million years.

The model contains a 2D ice sheet (Glen's Law solved with a semi-implicit scheme), an energy balance for the atmosphere and planet surface (explicit), and an ODE for the time evolution of CO2 (explicit).

The dependencies between these models generate behaviour similar to weakly coupled nonlinear oscillators.