Vincenzo Mantova (University of Leeds) – Globally Valued Fields (Part III)

Globally valued fields were introduced by Ben Yaacov and Hrushovski to capture the model theory of 'global fields with heights' in continuous logic. They subsequently proved that the algebraic closure of rational functions, with the usual projective heights, is existentially closed, while Szachniewicz proved the same for the field of algebraic numbers. I will give a minimal introduction to global fields and heights, keeping the presentation as close as possible to valuation theory, and to continuous logic, then explain what existential closedness means and how it relates to existing problems in Diophantine geometry. The talks are very loosely based on a small subsets of the 'foundations' paper by Ben Yaacov, Destic, Hrushovski, Szachniewicz and various other notes.