  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 at $n$ distinct times has in particular a
relatively simple expression as a function of $n$ variables on the Riemann
surface built from exponentials of Abelian integrals, traced over the ramified
covering and integrated on $n$ nested contours in the complex plane.
