Relations Between Solutions of ODEs and Model Theory

This conference talk by Léo Jimenez explores the mathematical question of whether differential-algebraic relations exist between generic tuples of solutions from two algebraic ordinary differential equations (ODEs). Discover the research conducted with Freitag and Moosa that establishes a bound on the tuple length needed to identify such relations. Learn about the dual foundations of the proof: differential Galois theory combined with the Freitag-Moosa proof of the Borovik-Cherlin conjecture in algebraically closed fields, and model theory techniques for factoring relations through minimal ODEs. Understand why the established bound is mathematically tight and cannot be improved. The talk was recorded during the thematic meeting "Galois differential Theories and transcendence" on February 20, 2025, at the Centre International de Rencontres Mathématiques in Marseille, France. This video is available in CIRM's Audiovisual Mathematics Library (http://library.cirm-math.fr), which offers features like chapter markers, keywords, abstracts, bibliographies, and multi-criteria search capabilities.