This is a joint work with Ronald Bustamante Medina and Zoé Chatzidakis. In this talk we are interested in differential and difference fields from the model-theoretic point of view. A differential field is a field with a set of commuting derivations and a difference-differential field is a differential field equipped with an automorphism which commutes with the derivations. Cassidy studied definable groups in differentially closed fields, in particular she studied Zariski dense definable subgroups of simple algebraic groups and showed that they are isomorphic to the rational points of an […]

A core question in the model theory of fields is to understand how combinatorial patterns and algebraic properties interact. The study of NIPn fields, which can't express the edge relation of random n-hypergraph, is linked to henselianity. In this talk, we use Chernikov and Hils conditions to obtain transfer in some situations, that is, under some algebraic assumptions, it is enough to know that the residue field of a henselian valued field is NIPn in order to known that it is itself NIPn, and we discuss consequences on hypothetical strictly […]