Leo Jimenez : Splitting differential equations using Galois theory

Posted by James Freitag , part of the Unlikely Intersections Seminar.

At

Nov. 14, 2023, 4 p.m.

In

636 SEO

Abstract

An ordinary algebraic differential equation is said to be internal to the constants if its general solution is obtained as a rational function of finitely many of its solutions and finitely many constant terms. Any such equation has an algebraic group acting as its Galois group. In this talk, I will use decomposition theorems for algebraic groups to show that some internal equations (do not) split into a product of internal equations. The methods are model-theoretic and could be applied to other contexts. This is a joint work in progress with Christine Eagles.