Bethe ansatz for models in the KPZ universality class
The KPZ universality class is one of the most active probability research areas in recent years. Models within this universality class include random matrices, random polymers, random walks, particle systems, stochastic differential equations, etc. One of the methods to establish the solvability of these models is based on Bethe's ansatz, proposed by Hans Bethe in 1931 to solve the one-dimensional antiferromagnetic Heisenberg model. Since then the method has been adapted to various models in statistical physics, quantum mechanics, and probability. In this talk we will see how this method allows us to obtain exact formulas for certain random walks, random polymers and particle systems within the KPZ universality class.