abstract: The "short Reeb orbit conjecture" states that on any closed three-manifold with a contact form, there is always a Reeb orbit of length no longer than the square root of the contact volume. This was recently disproved by Abbondandolo, Bramham, Hryniewicz, and Salomão. Hutchings, Ramos and I used Seiberg-Witten theory to prove an asymptotic version of this conjecture, however. I will explain our proof.