The KPZ universality class contains one dimensional growth models,
directed random polymers, stochastic Hamilton-Jacobi equations (e.g. the eponymous Kardar-Parisi-Zhang equation,
which led to a 2014 Fields medal). It is characterized by unusual scale of fluctuations, some of
which, surprisingly, come from random matrix theory, and which are model independent but do depend on the initial data.
The physical explanation is that in the space of Markov processes, these models are all being rescaled to a universal fixed point.
But this scaling invariant fixed point was completely unknown, even by the physicists, until this year, when we
managed to compute it in joint work with Konstantin Matetski
and Daniel Remenik. It is a new type of “stochastic integrable system”. In the talk I will describe it, as well
as how it was obtained by solving a special model in the class called TASEP.