Survey on some aspects of the arithmetic of complex local systems

Abstract:  Over the last few years I studied with Michael Groechenig, Moritz Kerz and in part with Johan de Jong properties of complex local systems on smooth quasi-projective varieties which are expected by Simpson’s general conjectures to be motivic.  It is a mathematical program. I’ll try to give an overview of some of the problems which are currently on my mind.  Best would be if we could develop the talk a bit  like a discussion. Feel free to ask questions, I‘ll try to think of them and, if possible, to answer.