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The KPZ universality class contains one dimensional growth models, directed random polymers, stochastic Hamilton-Jacobi equations (e.g. the eponymous Kardar-Parisi-Zhang equation).ÌýIt is characterized by unusual scale of fluctuations, some ofÌýwhich, surprisingly, come from random matrix theory, and which are model independent but do depend on the initial data.ÌýThe physical explanation is that in the space of Markov processes, these models are all being rescaled to a universal fixed point.ÌýBut this scaling invariant fixed point was completely unknown, even by the physicists, until this year, when weÌýmanaged to compute it in joint work with Konstantin MatetskiÌýand Daniel Remenik. It is a new type of integrable Markov process.Ìý In the talk I will describe it, as wellÌýas how it was obtained by solving a special model in the class called TASEP.