# Mathematics Colloquia and Seminars

I will discuss the higher spin six vertex model - an interacting  particle system on the discrete 1d line in the Kardar--Parisi--Zhang universality class. Observables of this system admit explicit contour integral expressions which degenerate  to many known formulas of such type for other integrable systems on the line in the KPZ class, including stochastic six vertex model, ASEP, various $q$-TASEPs, and associated zero range processes. The structure of the higher spin six vertex model (leading to contour integral formulas for observables) is based on Cauchy summation identities for certain symmetric rational functions, which in turn can be traced back to the sl2 Yang--Baxter equation. This framework allows to also include space and spin inhomogeneities into the picture, which leads to new particle systems with unusual phase transitions.