I will present the ODE/IM correspondence in its most simple incarnation: the Liouville model. After reviewing the known results, I will shift the point of view to a geometric interpretation of the Liouville equation. The aim is to exploit the geometric structure underlying the classical integrable equations to gain a deeper understanding of the ODE/IM correspondence. I will then move to describe the “massive” version of the correspondence. If time allows I will briefly talk about possible generalizations to supersymmetric models and \(T\bar T\)-deformed equations.

A visita do orador é financiada pelo projeto PTDC/MAT-STA/0975/2014.