SC4.10

In order to be able to have predictive power on extreme events we need to rely on mathematical approaches that provide us with some degree of universality, so that we have rigorous ways to extrapolate information beyond what has been already recorded. In this short course we will introduce frameworks based on dynamical systems theory and statistical mechanics that allow for a rigorous and effective treatment and analysis of extreme events. We will show how extreme value theory and large deviation theory allows for a better understanding of high-impact weather and climate extremes as well as of the basic dynamical properties of the atmosphere. We will introduce the basic theory and show applications on a range of datasets, including outputs of numerical models of various levels of complexity as well as observational data.