Hitchin's connection, originally constructed using techniques of Kähler geometry, is a flat projective connection on bundles of non-abelian theta functions. In this talk we will discuss its construction in algebraic geometry, and notably also for ground fields of (almost any) positive characteristic. Time permitting we will also discuss applications to higher rank Prym varieties.

This is joint work with M.Bolognesi, J.Martens and C.Pauly.