The project focuses on stochastic growth models in the Kardar-Parisi-Zhang universality class and closely related models such as random tiling models, with focus on their universal large time scaling limits, many of which describe the limiting laws for eigenvalues of random matrices. The goal of this project is to unravel the structure of the correlations in space-time of interfaces belonging to the KPZ universality class for generic boundary and initial conditions, as well as for vector-valued height functions.