Globally Valued Fields, studied jointly with E. Hrushovski, are a formalism for fields in which the sum formula for valuations holds, such as number fields or function fields of curves. They form an elementary class (in continuous first order logic), and model-theoretic questions regarding this class give rise to difficult yet fascinating geometric questions.
I intend to present « Lyon school » approach to studying GVFs. This consists of reducing as much as possible to local considerations, among other things via the "fullness" axiom.
- Logic Seminar