Francesco Gallinaro (University of Pisa)

Valued difference fields: amalgamation and existential closedness

A valued difference field is a valued field equipped with an automorphism which fixes the valuation ring setwise. I will discuss various properties of the existentially closed valued difference fields, both from the algebraic and the model-theoretic perspective, and I will highlight the role of tropical geometry in some of the proofs. This is joint work with Jan Dobrowolski and Rosario Mennuni.