Huh–Sturmfels conjecture on the maximum likelihood degree

Let $X$ be a closed irreducible subvariety of the hyperplane $H=\{(p_1,\ldots,p_n)\in({\mathbb{C}}^*)^n:p_1+\cdots+p_n=1\}$, and let $d=\dim X$. The Huh–Sturmfels conjecture. One has

$$(-1)^d\chi(X)\geq \operatorname{MLdeg}(X).$$

In particular, the topological signed Euler characteristic $(-1)^d\chi(X)$ is always nonnegative. This conjecture extends the equality $(-1)^d\chi(X)=\operatorname{MLdeg}(X)$ known for smooth very affine varieties to possibly singular subvarieties of the statistical hyperplane.