Christian d'Elbée, University of Bonn

The theory of fields expanded by a unary function symbol for a multiplicative endomorphism admits a model-companion, we denote it ACFH. It is a new example of an NSOP1 theory which is not simple. I will mention some features that appear in ACFH, notably a conjecturally suboptimal description of Shelah's forking and the ubiquity of definable groups whiches theories are pseudofinite-cyclic, that is, elementary equivalent to an ultraproduct of finite cyclic groups.