3 problems

Garren–Boozer conjecture. Non-axisymmetric but perfectly quasisymmetric stellarators cannot exist.

A quasisymmetric vector field is a vector field satisfying the quasisymmetry conditions in a toroidal domain; the relevant construction reduces to solving a first-order nonlinear p…

Negative-definiteness conjecture. The Hessian ${\bf H}({\bf a})$ is negative definite for all ${\bf a}\in\mathbb{R}^I$ satisfying those parameter conditions.