Amador Martin-Pizarro:
Model theory, differential algebra and functional transcendence
Zeit und Ort
Freitag, 21.11.25, 10:30-12:00, Seminarraum 404
Zusammenfassung
A fundamental problem in the study of algebraic differential equations is determining the possible algebraic relations among different solutions of a given differential equation. Freitag, Jaoui, and Moosa have isolated an essential property, called property D2, in order to show that if a differential equation given by an irreducible differential polynomial of order n is defined over the constants and has property D2, then any number of pairwise
distinct solutions together with their derivatives up to order n-1 are algebraically independent. The property D2 requires that, given two distinct solutions, there is no non-trivial algebraic dependence between the solutions and their first n-1 derivatives.
The proof of Freitag, Jaoui and Moosa is extremely elegant and short, yet it uses in
a clever way fundamental results of the model theory of differentially closed fields of
characteristic 0. The goal of this talk is to introduce the model-theoretic tools at the core
of their proof, without assuming a deep knowledge in (geometric) model theory (but
some familiarity with basic notions in algebraic geometry).