Prym varieties are abelian varieties similarly associated to a double covers of algebraic curves as Jacobians are to a curve. In this talk, we define a higher rank analogue of Prym varieties and investigate some of their geometric properties. In particular we are interested in deformation theoretic aspects that permit the construction of a generalized Hitchin's connection in this setting.

This talk is based on joint work in progress with Michele Bolognesi, Johan Martens and Christian Pauly.