#### Conference abstracts

Session B3 - Symbolic Analysis - Semi-plenary talk

July 15, 14:30 ~ 15:20 - Room B2

## The Good, the Bad, and the Ugly: the Cartan algorithm for overdetermined PDE systems

### Jeanne Clelland

In this talk, we will illustrate the application of Cartan's algorithm to the problem of finding strong Beltrami fields with nonconstant proportionality factor, i.e., vector fields $\mathbf{u}$ on an open set $U \subset \mathbb{R}^3$ with the property that $\nabla \times \mathbf{u} = f \mathbf{u}, \qquad \nabla \cdot \mathbf{u} = 0$ for some nonconstant function $f:U \to \mathbb{R}$. This example illustrates both the power of the method and some significant challenges that may arise during its application.