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This lecture explores the asymptotic expansion of free energy in confined planar Coulomb gases as the number of particles approaches infinity. Examine how the geometry of the confining set affects this expansion, particularly when the set is a Jordan domain, curve, or arc. Discover the relationship between this problem and Grunsky operators, and learn about connections to Loewner energy and other domain functionals. The presentation is based on joint research with K. Courteaut (NYU) and K. Johansson (KTH) and provides mathematical insights into the behavior of charged particles confined to sets in the complex plane.
