abstract: The Ruelle resonances of a dynamical system are spectral characteristics of a system, describing the precise asymptotics of correlations. While their existence can often be shown by abstract spectral analysis arguments, it is in general not possible to compute them exactly. I will explain that, in the case of linear pseudo-Anosov maps, they can be completely described in terms of the action of the map on cohomology. Joint work with Frédéric Faure and Erwan Lanneau