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A central challenge in statistical physics is to describe non-equilibrium systems driven by randomness, such as a randomly growing interface. Over time and after zooming out, such an interface will generally approach a deterministic limiting shape. Random fluctuations around this limit shape are believed to be universal in scale and statistical description, depending on the growth mechanism and randomness only via simple scaling parameters. This vision, put forward by Kardar, Parisi and Zhang (KPZ) in 1986, captured the imagination of physicists and more recently that of mathematicians.;The purpose of this program is to bring together mathematicians and physicists working on various aspects of KPZ integrability (e.g. quantum integrable systems, Bethe ansatz, Macdonald processes, algebraic combinatorics) and universality (e.g. stochastic partial differential equations, interacting particle systems, replica methods, random matrix theory), as well as create engagement between them and physicists working on applications and experiments (e.g. out of equilibrium transport, multi-component KPZ, higher dimensional growth and directed polymers, quantum quenches, bio-physics, other front equations, disordered and quenched KPZ). Ultimately this should promote the development of new concepts and methodologies across the study of non-equilibrium random systems.