Sturmfels–Uhler polynomiality conjecture for the maximum likelihood degree

Let $V$ be a vector space, let $\boldsymbol{S}^2V$ denote the space of symmetric matrices on $V$, and let $c6(n,a)$ be the maximum likelihood degree associated with symmetric matrices of size $n$ and a general $a$-dimensional linear subspace. Sturmfels and Uhler suggest that, for fixed $a$, this invariant is polynomial in $n$. Sturmfels\Uhler's polynomiality conjecture. For fixed $a$ the function $c6(n,a)$ is a polynomial in $n$ of degree $a-1$. The theorem preceding the conjecture establishes the formula in several low-dimensional cases and gives all values for $n\leq 6$; the conjecture is presented as an extrapolation from these known values and remains unresolved in the supplied text.