Terao's freeness conjecture for hyperplane arrangements

Let ${\mathcal{A}}_1$ and ${\mathcal{A}}_2$ be central hyperplane arrangements defined over the same field. Their intersection lattices $L({\mathcal{A}}_1)$ and $L({\mathcal{A}}_2)$ encode the same combinatorics when

$$L({\mathcal{A}}_1)\cong L({\mathcal{A}}_2).$$

For an arrangement ${\mathcal{A}}$, let $D({\mathcal{A}})$ denote its module of logarithmic derivations. Terao's conjecture. The derivation module $D({\mathcal{A}}_1)$ is free if and only if $D({\mathcal{A}}_2)$ is free. This conjecture asks whether freeness of the logarithmic derivation module is determined by the combinatorics of a central arrangement over a fixed field. It is a long-standing open problem in the theory of hyperplane arrangements.