The Hilbert Nullstellensatz provides a bridge between algebra and geometry, which becomes all the more concrete for examples of algebraically closed fields like the complex numbers. What are analogues of this situation in differential algebra?

In our talk, we will survey closed function spaces for the resolution of different types of differential equations: linear partial differential equations, asymptotic differential equations, recursive linear differential equations, and non-linear ordinary differential equations. We will also show some applications of having these concrete examples of closed function spaces.

Occasion: FOCM 2026, Vienna, Austria, July 16, 2026

Documents: slideshow, TeXmacs source