Six lectures on model theory and differential-algebraic geometry

TL;DR

This paper provides an accessible introduction to the model theory of differential fields, emphasizing differential-algebraic geometry, birational geometry of algebraic vector fields, and D-varieties, aimed at researchers in pure and applied model theory.

Contribution

It offers a concise overview connecting model theory with differential-algebraic geometry, focusing on birational geometry of algebraic vector fields and D-varieties.

Findings

Highlights the role of model theory in understanding differential-algebraic geometry

Explores birational geometry of algebraic vector fields and D-varieties

Provides foundational insights for further research in the field

Abstract

This is a write-up of some lectures I gave in the Fall of 2021 at the Fields Institute in Toronto, as part of the Thematic Programme on Trends in Pure and Applied Model Theory. The goal of the module was to give a quick introduction to the model theory of differential fields that puts differential-algebraic geometry at the center. I focus here on the birational geometry of algebraic vector fields and more generally $D$-varieties in the sense of Buium.