Joint Analysis and Probability seminar and KASS seminar

Abstract: Consider a logarithmic Coulomb gas constrained to a Jordan domain in the complex plane. How does the asymptotic expansion of the free energy depend on the geometry of the domain, as the number of particles tends to infinity? I will explain how this problem is related to the Grunsky operator -- a classical tool in complex analysis -- and how this in turn reveals a close connection to the Loewner energy and other interesting domain functionals. I will also discuss the analogous problem for a Jordan arc. This is based joint works with K. Courteaut (NYU) and K. Johansson (KTH).