The BMV conjecture

Let $A$ and $B$ be positive definite matrices, and let $n$ be a positive integer. The BMV conjecture. The polynomial in $t$

$$\operatorname{trace}\bigl(I+(A+tB)^n\bigr)$$

has all positive coefficients. The source presents this as the Bessis--Moussa--Villani conjecture in the reformulation of Lieb and Seiringer; no resolution is supplied in the cited passage.