Riemann surface for TASEP with periodic boundaries

The Bethe ansatz solution of periodic TASEP is formulated in terms of a ramified covering from a Riemann surface to the sphere. The joint probability distribution of height fluctuations atndistinct times has in particular a relatively simple expression as a function ofnvariables on the Riemann surface built from exponentials of Abelian integrals, traced over the ramified covering and integrated onnnested contours in the complex plane.