2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/50038We review the concept of $τ$-function for simple analytic curves. The $τ$-function gives a formal solution to the 2D inverse potential problem and appears as the $τ$-function of the integrable hierarchy which describes conformal maps of simply-connected domains bounded by analytic curves to the unit disk. The $τ$-function also emerges in the context of topological gravity and enjoys an interpretation as a large $N$ limit of the normal matrix model.13 pages, no figures, prepared for Proccedings of MSRI Workshop ``Matrix Models and Painlevé Equations'', Berkeley (USA) 1999High Energy Physics - Theorytext