Joakim Roos: Concepts in potential theory: equilibrium measures, balayage and quadrature domains

Classical potential theory was initially developed as a mathematical treatment of problems in Newtonian gravity and electrostatics and is, in essence, the study of harmonic functions and the Laplace operator. However, potential theory is in many ways intimately related to both probability theory and measure theory, and in this talk we will discuss a few concepts and methods in potential theory with a view towards the latter connection to measures. We will in particular treat equilibrium measures and balayage measures, present some results relating these concepts, and give an introduction to the topic of quadrature domains.