Large deviations in Coulomb gases: A mathematical perspective

These notes account for five ninety-minute lectures given by Mylène Maïda as part of the 2024 Summer School in Les Houches. This 4-week program was entitled Large deviations and applications. The goal of these lectures is to present a series of mathematical results about large deviations of the particles of a Coulomb gas or related systems, such as the eigenvalues of some random matrix ensembles. It encompasses the deviations of the empirical measure and those of the rightmost particle (corresponding to the largest eigenvalue).