Title: On the completeness of the Bethe ansatz for the periodic ASEP model.

Abstract: In recent work with collaborators Norman Do (Monash Uni.) and Eric Brattain (UC Davis), we have shown that the Bethe ansatz is complete for the periodic ASEP model. The ASEP model is a continuous Markov process which describes a system of N particles on a ring lattice of L sites and each particle has probability p (resp. 1-p) to jump right (resp. left). In our work, we use ideas from topology and complex geometry to obtain our results. I will expose the ideas behind this methods and discuss the applications of this methods for future work in scaling limits and the KPZ universality class.