Splitting the differential logarithm map using Galois theory

Christine Eagles, Department of Pure Mathematics, University of Waterloo

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. Such equations give rise to algebraic groups behaving as Galois groups. In this talk I give a characterisation of when the pullback of the differential logarithm of an equation is internal to the constants when the Galois group is unipotent or a torus. This is joint work in progress with Leo Jimenez.

MC 5479