By Louis-Pierre Arguin, Université de Montréal

The study of the distributions of extrema of a large collection of random variables dates back to the early 20th century and is well established in the case of independent or weakly correlated variables. Until recently, few sharp results were known in the case where the random variables are strongly correlated. In the last few years, there has been conceptual progress in describing the distribution of extrema of log-correlated Gaussian fields. This class of fields includes important examples such as branching Brownian motion and the 2D Gaussian free field. In this series of lectures, we will study the statistics of extrema of log-correlated Gaussian fields. The focus will be on explaining the guiding principles behind the results. We will use the example of branching Brownian motion to illustrate the method.