Fredrik Viklund: Free energy of a Coulomb gas on a Jordan domain

Abstract:

I will report on recent joint work with Kurt Johansson. We consider a Coulomb gas restricted to a Jordan domain in the complex plane. We ask how the asymptotic expansion of the free energy, as the number of particles tends to infinity, depends on the geometry of the domain. 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 further discuss the effect of corners, which turns out to be universal in a certain sense. Most main players (Grunsky, Loewner, etc) will be introduced in the talk.