Wojciech Gajda (UAM) Title: Semisimplicity of reductions and adelic openness for compatible systems over global function fields Abstract: I'll discuss some of highlights of my recent work (joint with G.Böckle and S.Petersen - to appear in the TAMS) on: - semi simplicity of the system of geometric residual Galois representations attached to cohomologies of an algebraic variety; - open image theorem over the adeles, for such a system of reps.