## Stahl's Theorem (aka BMV Conjecture): Insights and Intuition on its Proof and Applications

The Bessis-Moussa-Villani conjecture states that the trace of exp(A-tB) is, as a function of the real variable t, the Laplace transform of a positive measure, where A and B are hermitian matrices. The long standing conjecture was recently proven by Stahl and streamlined by Eremenko. We report on that proof and recall the significance of the result when approximating the energy of perturbed quantum mechanical systems.