On the Open 2–TASEP: Integrable Boundaries and speed of a single impurity

• Luigi Cantini (Université de Cergy-Pontoise)

The 2–TASEP (Two-Species Totally Asymmetric Simple Exclusion Process) is a natural multispecies generalization of the well-known TASEP. It involves two types of particles: one species moves exclusively to the right, the other to the left, with neighboring particles of different species exchanging positions upon encounter. In this talk, I will first discuss results related to the stationary measure of the model on a finite strip with integrable boundary conditions. Next, I will explore an alternative interpretation of the model's dynamics, where the left-moving particles are viewed as empty sites, while the original empty sites represent impurities. In this framework, I will address questions concerning the system's behavior in the presence of a single impurity on $\mathbb{Z}$. Work partially done in collaboration with Ali Zahra.

Ising-decorated cubic maps in arbitrary genus, bipartite maps, and the KP hierarchy

• Ariane Carrance (University of Vienna)

The generating function of bipartite maps in arbitrary genus is known to satisfy the integrable Kadomtsev--Petviashvili (KP) hierarchy. In this talk, I will explain how this powerful integrability property can be used to study another model of maps with more structure, namely Ising-decorated cubic maps. In particular, this leads to some inequalities on the enumeration coefficients, that are an important step in the study of Ising maps in high genus. This is based on a joint work in progress with Mireille Bousquet-Mélou and Baptiste Louf.