Abstract: The Coulomb gas is an interacting particle system with interesting behavior that has attracted a lot of mathematical research interest in the past 20 years, with applications to random matrix theory, numerical analysis, and plasma and solid-state physics. In this survey, we will introduce the basics of what the Coulomb gas is and why we care. We will discuss some fundamental results concerning the behavior of the gas, and how interesting tools in probability and differential equations can be useful.
This talk is geared towards a general mathematical audience. While some familiarity with introductory probability is helpful for intuition, all relevant ideas and concepts will be reviewed.
And, of course, there will be free pizza!